Filed Pursuant to Rule 424(b)(3)

Registration No. 333-295377

Proxy Statement/Prospectus Supplement No. 1

(to the Proxy Statement/Prospectus dated June 17, 2026)

SUPPLEMENT TO

PROXY STATEMENT FOR EXTRAORDINARY GENERAL MEETING OF

PERCEPTIVE CAPITAL SOLUTIONS CORP

AND

PROSPECTUS FOR UP TO 82,313,492 SHARES

OF COMMON STOCK OF PERCEPTIVE CAPITAL SOLUTIONS CORP

(AFTER ITS DOMESTICATION AS A CORPORATION INCORPORATED IN THE STATE OF

DELAWARE, WHICH WILL BE RENAMED FREENOME, INC. IN CONNECTION WITH THE

DOMESTICATION DESCRIBED HEREIN)

In connection with the proposed business combination among Perceptive Capital Solutions Corp (“PCSC”), StarNet Merger Sub I, Corp., a Delaware corporation and wholly-owned subsidiary of PCSC (“Merger Sub I”), StarNet Merger Sub II, LLC, a Delaware limited liability company and wholly-owned subsidiary of PCSC (“Merger Sub II”) and Freenome Holdings, Inc., a Delaware corporation (“Freenome”), upon the consummation of which PCSC will be renamed “Freenome, Inc.” (“PubCo”), PCSC and Freenome filed a registration statement on Form S-4 (File No. 333-295377) (as amended and supplemented, the “Registration Statement”) with the U.S. Securities and Exchange Commission (the “SEC”). The Registration Statement, which was declared effective by the SEC on June 17, 2026, includes a proxy statement/prospectus (the “Proxy Statement/Prospectus”). This Supplement No. 1, dated July 9, 2026 (this “Supplement”), updates and supplements the Proxy Statement/Prospectus.

The purpose of this Supplement is to update and supplement certain information contained in the Proxy Statement/Prospectus to (i) reflect recent developments that occurred after the date of the Proxy Statement/Prospectus, (ii) postpone the date and time of the extraordinary general meeting to 10:00 a.m. Eastern Time, on July 15, 2026, at the offices of Cooley LLP located at 55 Hudson Yards, New York, New York 10001, and via a virtual meeting at https://www.cstproxy.com/perceptivecapitalsolutions/sm2026; and (iii) extend the redemption deadline to no later than 5:00 p.m., Eastern Time, on July 13, 2026 (two business days prior to the scheduled vote at the extraordinary general meeting). Except as otherwise set forth below, the information set forth in the Proxy Statement/Prospectus remains unchanged. For clarity, additions to existing disclosure from the Proxy Statement/Prospectus are indicated with bold, underlined text. All page, paragraph and section references used herein refer to the Proxy Statement/Prospectus before any additions or deletions resulting from the revised disclosures, and capitalized terms used but not otherwise defined herein have the meanings ascribed to them in the Proxy Statement/Prospectus.

The information set forth below serves as a supplement to the Proxy Statement/Prospectus. Except as described herein, the information provided in the Proxy Statement/Prospectus continues to apply. To the extent this Supplement differs from or updates information in the Proxy Statement/Prospectus, shareholders should rely on the information contained in this Supplement. The Proxy Statement/Prospectus contains important additional information. This Supplement should be read in conjunction with the Proxy Statement/Prospectus.

You should read carefully and in their entirety this Supplement and the Proxy Statement/Prospectus and all accompanying annexes and exhibits before voting your PCSC Shares. Please pay particular attention to the section entitled “Risk Factors” beginning on page 25 in the Proxy Statement/Prospectus.

NEITHER THE SEC NOR ANY STATE SECURITIES COMMISSION HAS APPROVED OR DISAPPROVED OF THE BUSINESS COMBINATION (AS DEFINED IN THE PROXY STATEMENT/PROSPECTUS) OR THE OTHER TRANSACTIONS CONTEMPLATED THEREBY, OR PASSED UPON THE ADEQUACY OR ACCURACY OF THE DISCLOSURE IN THE PROXY STATEMENT/PROSPECTUS. ANY REPRESENTATION TO THE CONTRARY IS A CRIMINAL OFFENSE.

UPDATES TO DETAILS OF THE EXTRAORDINARY GENERAL MEETING

The following amends and supplements the disclosure throughout the Proxy Statement/Prospectus where applicable.

Date, Time and Place

With the filing of this Supplement, the extraordinary general meeting will now be held at 10:00 a.m., Eastern Time, on July 15, 2026, at the offices of Cooley LLP located at 55 Hudson Yards, New York, New York 10001, and via a virtual meeting at https://www.cstproxy.com/perceptivecapitalsolutions/sm2026.

Shareholders may attend the extraordinary general meeting in person. If you wish to attend the extraordinary general meeting in person at the offices of Cooley LLP located at 55 Hudson Yards, New York, New York 10001, you must reserve your attendance at least two business days in advance of the extraordinary general meeting by contacting PCSC’s secretary at PCSC@perceptivelife.com by 10:00 a.m., Eastern Time, on July 13, 2026.

Any previously submitted voting proxies by a public shareholder in connection with the proposed Business Combination may be revoked and resubmitted at any time prior to the polls being closed at the extraordinary general meeting held at 10:00 a.m., Eastern Time, on July 15, 2026, provided that any proxy not so revoked and resubmitted shall remain valid and in full force and effect.

With the filing of this Supplement, public shareholders who seek to redeem their public shares will now have until 5:00 p.m., Eastern Time, on July 13, 2026 (two business days prior to the scheduled vote at the extraordinary general meeting) to demand redemption of their public shares. Any redemption requests previously submitted by a public shareholder in connection with the proposed Business Combination may be withdrawn at any time prior to 5:00 p.m., Eastern Time, on July 13, 2026, provided that any redemption request not so withdrawn shall remain valid and in full force and effect.

UPDATES TO INFORMATION ABOUT FREENOME

The last full paragraph under the subsection “SimpleScreen v2 — Comprehensive Upgrade of v1 to Drive Potentially Best-In-Class Performance Amongst Blood-Based CRC Screening Tests” shall be revised to read as follows:

Additional improvements in the updated test included increased sensitivity of 44% for APLs with high-grade dysplasia, a 2.6-fold reduction in the limit of detection, and meaningful improvements in projected patient outcomes (9% reduction in lifetime CRC cases and 10% reduction in CRC deaths). V2 will continue to be evaluated in analytical and clinical validation studies. For example, in July 2026, we announced results from a pivotal clinical validation study that assessed the performance of assay and algorithm improvements.  The study successfully met its primary and secondary endpoints. The updated test showed 18.2% sensitivity in detecting advanced precancerous lesions (“APLs”), 41.9% sensitivity for APLs with high-grade dysplasia (“HGD”), and 80.4% sensitivity in detecting CRC, including 52% of Stage I cases (Stage I (T1) 39.9% and Stage I (T2) 81.2%), 100% of Stage II, 97.3% of Stage III and 100% of Stage IV. The results were adjusted to the age and sex distribution of the U.S. Census to better reflect the intended use population, and specificity for no findings on colonoscopy was 90%. The data are preliminary, and management’s review and analysis are ongoing.

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