UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

SCHEDULE 13D

Under the Securities Exchange Act of 1934

(Amendment No. 7)*

R1 RCM INC.

(Name of Issuer)

Common Stock, par value $0.01 per share

(Title of Class of Securities)

77634L 105

(CUSIP Number)

Glenn Miller

c/o TowerBrook Capital Partners L.P.

Park Avenue Tower

65 East 55th Street, 19th Floor

New York, NY 10022

(212) 699-2200

Copy to:

Steven A. Cohen

Victor Goldfeld

Wachtell, Lipton, Rosen & Katz

51 West 52nd Street

New York, NY 10019

(212) 403-1000

Christine McCoy

c/o Ascension Health Alliance

101 S. Hanley Road, Suite 450

St. Louis, MO 63105

(314) 733-8000

Copy to:

Stephen A. Infante

Covington & Burling LLP

620 Eighth Avenue

New York, NY 10018

(212) 841-1000

(Name, Address and Telephone Number of Persons
Authorized to Receive Notices and Communications)

June 12, 2024

(Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§ 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box. ¨

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See § 240.13d-7 for other parties to whom copies are to be sent.

^* The remainder of this cover page shall be filled out for a reporting person’s initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (the “Exchange Act”) or otherwise subject to the liabilities of that section of the Exchange Act but shall be subject to all other provisions of the Exchange Act (however, see the Notes).

CUSIP No. 77634L 105

1.	NAMES OF REPORTING PERSONS TCP-ASC ACHI Series LLLP
2.	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (see instructions) (a)  x (b)  ¨
3.	SEC USE ONLY
4.	SOURCE OF FUNDS (see instructions)  OO
5.	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)     ¨
6.	CITIZENSHIP OR PLACE OF ORGANIZATION   Delaware

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH	7.	SOLE VOTING POWER   0
	8.	SHARED VOTING POWER   164,754,055 (1)
	9.	SOLE DISPOSITIVE POWER   0
	10.	SHARED DISPOSITIVE POWER 164,754,055 (1)

11.	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON Common Stock:  164,754,055 (1)
12.	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES (see instructions)     ¨
13.	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) Common Stock:  35.7% (1) (2)
14.	TYPE OF REPORTING PERSON (see instructions) PN

(1) Consists of 124,289,200 shares of Common Stock and 40,464,855 shares of Common Stock issuable upon exercise of the Warrant.

(2) For purposes of calculating beneficial ownership of the Reporting Person, the total number of shares of Common Stock outstanding is based on (1) 421,255,230 shares of Common Stock outstanding as of May 6, 2024 as reported by the Issuer in its Quarterly Report on Form 10-Q filed with the Securities and Exchange Commission (the “SEC”) on May 8, 2024 and (2) 40,464,855 shares of Common Stock issuable upon exercise of the Warrant (see Note 1).

CUSIP No. 77634L 105

1.	NAMES OF REPORTING PERSONS TCP-ASC GP, LLC
2.	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (see instructions) (a)  x (b)  ¨
3.	SEC USE ONLY
4.	SOURCE OF FUNDS (see instructions)  OO
5.	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)     ¨
6.	CITIZENSHIP OR PLACE OF ORGANIZATION   Delaware

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH	7.	SOLE VOTING POWER   0
	8.	SHARED VOTING POWER   164,754,055 (1)
	9.	SOLE DISPOSITIVE POWER   0
	10.	SHARED DISPOSITIVE POWER   164,754,055 (1)

11.	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON Common Stock:  164,754,055 (1)
12.	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES (see instructions)     ¨
13.	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) Common Stock:  35.7% (1) (2)
14.	TYPE OF REPORTING PERSON (see instructions) OO

(1) Consists of 124,289,200 shares of Common Stock and 40,464,855 shares of Common Stock issuable upon exercise of the Warrant.

(2) For purposes of calculating beneficial ownership of the Reporting Person, the total number of shares of Common Stock outstanding is based on (1) 421,255,230 shares of Common Stock outstanding as of May 6, 2024 as reported by the Issuer in its Quarterly Report on Form 10-Q filed with the SEC on May 8, 2024 and (2) 40,464,855 shares of Common Stock issuable upon exercise of the Warrant (see Note 1).

CUSIP No. 77634L 105

1.	NAMES OF REPORTING PERSONS TI IV ACHI Holdings GP, LLC
2.	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (see instructions) (a)  x (b)  ¨
3.	SEC USE ONLY
4.	SOURCE OF FUNDS (see instructions)  OO
5.	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)     ¨
6.	CITIZENSHIP OR PLACE OF ORGANIZATION   Delaware

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH	7.	SOLE VOTING POWER   0
	8.	SHARED VOTING POWER   164,754,055 (1)
	9.	SOLE DISPOSITIVE POWER   0
	10.	SHARED DISPOSITIVE POWER   164,754,055 (1)

11.	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON Common Stock:  164,754,055 (1) (3)
12.	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES (see instructions)     ¨
13.	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) Common Stock:  35.7% (1) (2)
14.	TYPE OF REPORTING PERSON (see instructions) OO

(1) Consists of 124,289,200 shares of Common Stock and 40,464,855 shares of Common Stock issuable upon exercise of the Warrant.

(2) For purposes of calculating beneficial ownership of the Reporting Person, the total number of shares of Common Stock outstanding is based on (1) 421,255,230 shares of Common Stock outstanding as of May 6, 2024 as reported by the Issuer in its Quarterly Report on Form 10-Q filed with the SEC on May 8, 2024 and (2) 40,464,855 shares of Common Stock issuable upon exercise of the Warrant (see Note 1).

(3) TI IV ACHI Holdings, LP disclaims beneficial ownership of 75,889,325 shares of Common Stock held directly by Series AS (as defined in Item 6 herein).

CUSIP No. 77634L 105

1.	NAMES OF REPORTING PERSONS TI IV ACHI Holdings, LP
2.	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (see instructions) (a)  x (b)  ¨
3.	SEC USE ONLY
4.	SOURCE OF FUNDS (see instructions)  OO
5.	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)     ¨
6.	CITIZENSHIP OR PLACE OF ORGANIZATION   Delaware

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH	7.	SOLE VOTING POWER   0
	8.	SHARED VOTING POWER   164,754,055 (1)
	9.	SOLE DISPOSITIVE POWER   0
	10.	SHARED DISPOSITIVE POWER   164,754,055 (1)

11.	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON Common Stock:  164,754,055 (1) (3)
12.	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES (see instructions)     ¨
13.	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) Common Stock:  35.7% (1) (2)
14.	TYPE OF REPORTING PERSON (see instructions) PN

(1) Consists of 124,289,200 shares of Common Stock and 40,464,855 shares of Common Stock issuable upon exercise of the Warrant.

(2) For purposes of calculating beneficial ownership of the Reporting Person, the total number of shares of Common Stock outstanding is based on (1) 421,255,230 shares of Common Stock outstanding as of May 6, 2024 as reported by the Issuer in its Quarterly Report on Form 10-Q filed with the SEC on May 8, 2024 and (2) 40,464,855 shares of Common Stock issuable upon exercise of the Warrant (see Note 1).

(3) TI IV ACHI Holdings GP, LLC disclaims beneficial ownership of 75,889,325 shares of Common Stock held directly by Series AS (as defined in Item 6 herein).

CUSIP No. 77634L 105

1.	NAMES OF REPORTING PERSONS TowerBrook Investors Ltd.
2.	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (see instructions) (a)  x (b)  ¨
3.	SEC USE ONLY
4.	SOURCE OF FUNDS (see instructions)  OO
5.	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)     ¨
6.	CITIZENSHIP OR PLACE OF ORGANIZATION   Cayman Islands

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH	7.	SOLE VOTING POWER   0
	8.	SHARED VOTING POWER   164,754,055  (1)
	9.	SOLE DISPOSITIVE POWER   0
	10.	SHARED DISPOSITIVE POWER   164,754,055 (1)

11.	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON Common Stock:  164,754,055 (1) (3)
12.	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES (see instructions)     ¨
13.	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) Common Stock:  35.7% (1) (2)
14.	TYPE OF REPORTING PERSON (see instructions) OO

(1) Consists of 124,289,200 shares of Common Stock and 40,464,855 shares of Common Stock issuable upon exercise of the Warrant.

(2) For purposes of calculating beneficial ownership of the Reporting Person, the total number of shares of Common Stock outstanding is based on (1) 421,255,230 shares of Common Stock outstanding as of May 6, 2024 as reported by the Issuer in its Quarterly Report on Form 10-Q filed with the SEC on May 8, 2024 and (2) 40,464,855 shares of Common Stock issuable upon exercise of the Warrant (see Note 1).

(3) TowerBrook Investors Ltd. disclaims beneficial ownership of 75,889,325 shares of Common Stock held directly by Series AS (as defined in Item 6 herein).

CUSIP No. 77634L 105

1.	NAMES OF REPORTING PERSONS Neal Moszkowski
2.	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (see instructions) (a)  x (b)  ¨
3.	SEC USE ONLY
4.	SOURCE OF FUNDS (see instructions)  OO
5.	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)     ¨
6.	CITIZENSHIP OR PLACE OF ORGANIZATION   U.S.A.

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH	7.	SOLE VOTING POWER   0
	8.	SHARED VOTING POWER   164,754,055 (1)
	9.	SOLE DISPOSITIVE POWER   0
	10.	SHARED DISPOSITIVE POWER   164,754,055 (1)

11.	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON Common Stock:  164,754,055 (1) (3)
12.	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES (see instructions)     ¨
13.	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) Common Stock:  35.7% (1) (2)
14.	TYPE OF REPORTING PERSON (see instructions) IN

(1) Consists of 124,289,200 shares of Common Stock and 40,464,855 shares of Common Stock issuable upon exercise of the Warrant.

(2) For purposes of calculating beneficial ownership of the Reporting Person, the total number of shares of Common Stock outstanding is based on (1) 421,255,230 shares of Common Stock outstanding as of May 6, 2024 as reported by the Issuer in its Quarterly Report on Form 10-Q filed with the SEC on May 8, 2024 and (2) 40,464,855 shares of Common Stock issuable upon exercise of the Warrant (see Note 1).

(3) Neal Moszkowski disclaims beneficial ownership of 75,889,325 shares of Common Stock held directly by Series AS (as defined in Item 6 herein).

CUSIP No. 77634L 105

1.	NAMES OF REPORTING PERSONS Jonathan Bilzin
2.	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (see instructions) (a)  x (b)  ¨
3.	SEC USE ONLY
4.	SOURCE OF FUNDS (see instructions)  OO
5.	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)     ¨
6.	CITIZENSHIP OR PLACE OF ORGANIZATION   U.S.A.

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH	7.	SOLE VOTING POWER   0
	8.	SHARED VOTING POWER   164,754,055 (1)
	9.	SOLE DISPOSITIVE POWER   0
	10.	SHARED DISPOSITIVE POWER   164,754,055 (1)

11.	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON Common Stock:  164,754,055 (1) (3)
12.	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES (see instructions)     ¨
13.	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11) Common Stock:  35.7% (1) (2)
14.	TYPE OF REPORTING PERSON (see instructions) IN

(1) Consists of 124,289,200 shares of Common Stock and 40,464,855 shares of Common Stock issuable upon exercise of the Warrant.

(2) For purposes of calculating beneficial ownership of the Reporting Person, the total number of shares of Common Stock outstanding is based on (1) 421,255,230 shares of Common Stock outstanding as of May 6, 2024 as reported by the Issuer in its Quarterly Report on Form 10-Q filed with the SEC on May 8, 2024 and (2) 40,464,855 shares of Common Stock issuable upon exercise of the Warrant (see Note 1).

(3) Jonathan Bilzin disclaims beneficial ownership of 75,889,325 shares of Common Stock held directly by Series AS (as defined in Item 6 herein).

CUSIP No. 77634L 105

1.	NAMES OF REPORTING PERSONS Karim Saddi
2.	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (see instructions) (a)  x (b)  ¨
3.	SEC USE ONLY
4.	SOURCE OF FUNDS (see instructions) OO
5.	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)     ¨
6.	CITIZENSHIP OR PLACE OF ORGANIZATION   France

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH	7.	SOLE VOTING POWER    0
	8.	SHARED VOTING POWER   164,754,055 (1)
	9.	SOLE DISPOSITIVE POWER 0
	10.	SHARED DISPOSITIVE POWER 164,754,055 (1)

11.	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON Common Stock:  164,754,055 (1) (3)
12.	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES (see instructions)     ¨
13.	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)  Common Stock:  35.7% (1) (2)
14.	TYPE OF REPORTING PERSON (see instructions) IN

(1) Consists of 124,289,200 shares of Common Stock and 40,464,855 shares of Common Stock issuable upon exercise of the Warrant.

(2) For purposes of calculating beneficial ownership of the Reporting Person, the total number of shares of Common Stock outstanding is based on (1) 421,255,230 shares of Common Stock outstanding as of May 6, 2024 as reported by the Issuer in its Quarterly Report on Form 10-Q filed with the SEC on May 8, 2024and (2) 40,464,855 shares of Common Stock issuable upon exercise of the Warrant (see Note 1).

(3) Karim Saddi disclaims beneficial ownership of 75,889,325 shares of Common Stock held directly by Series AS (as defined in Item 6 herein).

CUSIP No. 77634L 105

1.	NAMES OF REPORTING PERSONS ASCENSION HEALTH ALLIANCE
2.	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (see instructions) (a)  x (b)  ¨
3.	SEC USE ONLY
4.	SOURCE OF FUNDS (see instructions) OO
5.	CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT TO ITEMS 2(d) or 2(e)     ¨
6.	CITIZENSHIP OR PLACE OF ORGANIZATION   Missouri

NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH	7.	SOLE VOTING POWER    0
	8.	SHARED VOTING POWER   164,754,055 (1)
	9.	SOLE DISPOSITIVE POWER 0
	10.	SHARED DISPOSITIVE POWER 164,754,055 (1)

11.	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON Common Stock:  164,754,055 (1) (3)
12.	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES (see instructions)     ¨
13.	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)  Common Stock:  35.7% (1) (2)
14.	TYPE OF REPORTING PERSON (see instructions) CO

(1) Consists of 124,289,200 shares of Common Stock and 40,464,855 shares of Common Stock issuable upon exercise of the Warrant.

(2) For purposes of calculating beneficial ownership of the Reporting Person, the total number of shares of Common Stock outstanding is based on (1) 421,255,230 shares of Common Stock outstanding as of May 6, 2024 as reported by the Issuer in its Quarterly Report on Form 10-Q filed with the SEC on May 8, 2024 and (2) 40,464,855 shares of Common Stock issuable upon exercise of the Warrant (see Note 1).

(3) Ascension Health Alliance disclaims beneficial ownership of 88,864,730 shares of Common Stock held directly by Series TB (as defined in Item 6 herein).

This Amendment No. 7 to Schedule 13D (this "Amendment No. 7") amends and supplements the statement on Schedule 13D jointly filed by TCP - ASC ACHI Series LLLP (the "Partnership"), TCP - ASC GP, LLC, TI IV ACHI Holdings GP, LLC, TI IV ACHI Holdings, LP, TowerBrook Investors Ltd., Neal Moszkowski, Jonathan Bilzin, Karim Saddi and Ascension Health Alliance d/b/a Ascension (the "Reporting Persons") with the Securities Exchange Commission (the "Commission") on June 21, 2022, as amended on September 13, 2022, October 3, 2023, February 6, 2024, March 11, 2024, May 7, 2024 and June 3, 2024 (as it may be amended from time to time, this "Statement"), relating to the common stock, $0.01 par value per share (the "Common Stock"), of R1 RCM Inc. (the "Issuer"). Initially capitalized terms used in this Amendment No. 7 that are not otherwise defined herein shall have the same meanings attributed to them in the Schedule 13D. Except as expressly provided herein, all Items of the Schedule 13D remain unchanged.

ITEM 4. Purpose of the Transaction.

Item 4 of the Schedule 13D is hereby amended and supplemented as follows:

Pursuant to the May 6 Waiver, the Partnership, CoyCo and their respective affiliates have engaged in constructive discussions regarding their potential pursuit of a Joint Transaction. On June 12, 2024, the Partnership and CoyCo submitted a request to the Issuer (the "June 12 Waiver Request") to extend the waiver period under the May 6 Waiver through July 12, 2024. On June 13, 2024, the Issuer granted the waiver requested by the June 12 Waiver Request.

The foregoing description of the June 12 Waiver Request is not intended to be complete and is qualified in its entirety by reference to the full text of the June 12 Waiver Request. The June 12 Waiver Request is filed as Exhibit 7.11 hereto.

TowerBrook Capital Partners L.P., Ascension, and New Mountain Capital, L.L.C. have come to an understanding with respect to the sharing of certain expenses incurred in connection with the evaluation, negotiation, pursuit or consummation of a Joint Acquisition.

ITEM 7. Materials to be Filed as Exhibits.

The following document noted as Exhibit 7.11 is filed as an exhibit to this Statement:

Exhibit Number	Description of Exhibit
Exhibit 7.11	Waiver Extension Request, dated June 12, 2024.

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Date: June 12, 2024
TCP-ASC ACHI SERIES LLLP
By: TCP-ASC GP, LLC, its General Partner
By:	/s/ Glenn F. Miller
Name: Glenn F. Miller
Title: Vice President
TCP-ASC GP, LLC
By:	/s/ Glenn F. Miller
Name: Glenn F. Miller
Title: Vice President
TI IV ACHI Holdings GP, LLC
By:	/s/ Glenn F. Miller
Name: Glenn F. Miller
Title: Vice President

[Signature Page to 13D Amendment]

TI IV ACHI Holdings, LP
By: TI IV ACHI Holdings GP, LLC, its General Partner
By:	/s/ Glenn F. Miller
Name: Glenn F. Miller
Title: Vice President
TOWERBROOK INVESTORS LTD.
By:	/s/ Neal Moszkowski
Name: Neal Moszkowski
Title: Director
NEAL MOSZKOWSKI
/s/ Neal Moszkowski
Neal Moszkowski
JONATHAN BILZIN
/s/ Jonathan Bilzin
Jonathan Bilzin
KARIM SADDI
/s/ Karim Saddi
Karim Saddi

[Signature Page to 13D Amendment]

ASCENSION HEALTH ALLIANCE
By:	/s/ Christine McCoy
Name: Christine McCoy
Title: Executive Vice President & General Counsel

[Signature Page to 13D Amendment]