Exhibit 9

STRICTLY CONFIDENTIAL

VIA EMAIL

July 2, 2024

Members of the Special Committee of the Board of Directors

R1 RCM Inc.

434 W. Ascension Way, 6th Floor

Murray, Utah 84123

Attn: General Counsel

Dear Members of the Special Committee:

New Mountain Capital L.L.C. (“New Mountain”), on behalf of certain managed funds (collectively, the “New Mountain Funds”) is pleased to submit this non-binding proposal to acquire all of the outstanding shares of common stock of R1 RCM Inc., a Delaware corporation (the “Company”), that are not currently owned by CoyCo 1, L.P. a Delaware limited partnership (“CoyCo 1”), and CoyCo 2, L.P., a Delaware limited partnership (“CoyCo 2” and, together with CoyCo 1, the “Investors”) or their respective affiliates for cash consideration of $13.25 per share (our “Proposal”). As you know, the Investors are among the largest stockholders of the Company, collectively owning approximately 32% of the Company’s outstanding common stock.

We believe that our Proposal provides compelling value and immediate liquidity to the Company’s public stockholders. Specifically, $13.25 per share represents a significant premium of 30.3% to the closing price per share of $10.17 on January 25, 2024, the day prior to our initial request for a waiver of certain provisions of our Investor Rights Agreement, and a premium of 31.6% to the 30-day volume-weighted average price per share of $10.07 as of such date. As of February 23, 2024, the last trading day prior to our amended request for a waiver, $13.25 per share represented a more than 29.1% premium to the 30-day volume-weighted average price of $10.26.

We have completed our business due diligence and are prepared to move forward with completing definitive documentation and signing a transaction by July 12, 2024. The $13.25 per share price proposed herein reflects the completion of diligence and takes into account events that have occurred subsequent to our initial waiver request on January 26, 2024.

In addition to delivering significant and certain value to the Company’s existing stockholders, we believe that consummation of our proposed transaction will allow the Company to better focus on serving its customers and executing its long-term business plan without the distractions that come with operating as a public company. In a private context, with additional investment and value-added support from the New Mountain Funds, the Company would be able to efficiently execute on its objectives and deliver additional benefit to clients and employee stakeholders.

Our Proposal assumes a recapitalization of the Company’s indebtedness with new third-party debt financing from Goldman Sachs & Co. LLC and J.P. Morgan Securities LLC. We have received commitment letters and can share them with you at your request. The equity financing to support the Proposal would be funded by the rollover of the Investors’ existing 32% common stock ownership interest in the Company and new cash equity to be provided or arranged by the New Mountain Funds.

Prior to signing any definitive documentation, as part of customary pre-signing discussions with customers, we would expect to discuss with the Company’s current customer stockholders (Ascension Health, Intermountain, LifePoint Health, Providence and Sutter) their interest in maintaining or increasing their equity investment in the Company through new investment or through a rollover of all or a portion of their current common stock positions. In addition to current customer stockholders, we would also welcome having TowerBrook Capital Partners participate as a co-investor in the transaction. In order to provide certainty to the Company, our Proposal is not contingent on any current direct or indirect stockholders participating or rolling their existing ownership interest in the Company into the transaction.

This Proposal has been approved by New Mountain’s investment committee. We have completed our business due diligence and, based on our existing knowledge of the Company and our willingness to commit the time and resources necessary to complete the transaction, we are confident that with appropriate engagement by the Company and its advisors, we can expeditiously sign definitive documentation. Our Proposal remains subject to the negotiation and execution of mutually acceptable definitive agreements, and our counsel will share a draft merger agreement with the Special Committee’s advisors later today.

As required by their role as stewards of this process, we expect that the Special Committee will consider our Proposal promptly and make a recommendation to the full Board of Directors for their consideration in accordance with their fiduciary duties. The consummation of the transactions contemplated by our Proposal will be conditioned upon approval by both the Special Committee and the Board of Directors. Given our existing stake in and history with the Company, we are in a position to complete the transaction quickly. If and when approved by the Special Committee, we would also like to discuss with members of management whether they would have any interest in rolling over a portion of their equity in the transaction.

This Proposal is a non-binding expression of interest only, does not constitute an offer subject to binding acceptance, and is subject to execution of mutually acceptable definitive transaction documentation. We reserve the right to withdraw or modify our Proposal at any time. No legal obligation with respect to the Proposal or any other transaction shall arise unless and until we have executed definitive transaction documentation with the Company.

We have engaged Ropes & Gray LLP, Goldman Sachs & Co. LLC, and J.P. Morgan Securities LLC to advise us on this transaction.

We would appreciate the opportunity to discuss our Proposal with the Special Committee and its advisors as soon as possible. We and our advisors look forward to working with the Special Committee and the Board of Directors and their advisors to negotiate and consummate a mutually acceptable transaction. We are available at your convenience to discuss any aspects of our Proposal.

Sincerely,

New Mountain Capital L.L.C.
By:	/s/ Matthew S. Holt
Name: Matthew S. Holt
Title: Managing Director & President, Private Equity