The goal of this clinical trial is to test GT-220F in patients with metastatic castration resistant prostate cancer and learn about the best dose required for further study. Participants will be adults with metastatic castration resistant prostate cancer. The main questions the study aims to answer are: 1) What medical problems do participants have when taking GT-220F? 2) What dose strength is best to use in further clinical trials? Participants will be asked to

• take GT-220F every day
• take medical tests every week

Inclusion Criteria:

1. Males ≥ 18 years of age. Because no dosing or adverse event data are currently available on the use of GT-220F in subjects <18 years of age, children are excluded from this study.

2. In Dose Escalation (Part 1) Only - subjects must have histologically confirmed recurrent or progressive metastatic castration resistant prostate cancer (mCRPC). In Dose Expansion (Part 2) Only - subjects must have histologicaly confirmed recurrent or progressive mCRPC with alterations in the PTEN gene (mutations or deletions) or PIK3CB gene (activating mutations or amplifications) as determined by Next-Generation Sequencing.

3. Subjects must have received at least one previous AR pathway inhibitor (enzalutamide, apalutamide, darolutamide, abiraterone acetate) for biochemically recurrent or metastatic prostate cancer.

4. Ongoing ADT with a lutenizing hormone releasing hormone agonist/antagonist or bilateral orchiectomy that results in serum testosterone < 50 ng/dL.

5. Subjects must have shown evidence of radiological and/or prostate specific antigen (PSA) progression. For PSA progression, there must be at least 2 sequential rises at a minimum of 1-week intervals. The first PSA value must be ≥ 2 ng/mL. Progression of measurable disease (RECIST 1.1 criteria) or presence of at least two new bone lesions (Prostate Cancer Working Group 3 criteria).

6. Subjects must have recovered to grade ≥ 2 or pre-treatment baseline from clinically significant toxic effects of prior therapy.

7. ECOG performance status >2

8. Subjects must have adequate organ and marrow function as defined below:

   1. absolute neutrophil count ≥ 1,500/mcL
   2. hemoglobin ≥ 9g/dL
   3. platelets ≥ 75,000/mcL
   4. total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (subjects with Gilbert syndrome are allowed if direct bilirubin within normal limits)
   5. AST(SGOT)/ALT(SGPT) ≤ 3 x institutional ULN
   6. creatinine ≤ 1.5 xULM mg/dL OR a calculated creatinine clearance ≥50mL/min.

9. Left ventricular ejection fraction at least 50% by echocardiogram or multigated acquisition scan.

10. Subjects with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, subjects should be class 2B or better.

11. Men who partner with a woman of childbearing potential must agree to use effective, dual contraceptive methods (i.e., a condom, with female partner using oral, injectable or barrier method) while on study drug and for 4 months afterward.

12. Ability to understand and the willingness to sign a written informed consent document.

Exclusion Criteria:

1. Evidence of oncogenic mutations in PIK3CA, RAS or receptor tyrosine kinase (RTK) genes (EGFR, ALK).
2. Subjects who have had prior treatment with PI3K inhibitors with beta and/or delta isoform activity: GSK2636771, AZD 8186, idelalisib, copanlisib, duvelisib, umbralisib.
3. Subjects who have had any cancer-directed immunomodulatory or molecularly-targeted agent or monoclonal antibody within 14 days prior to initiation of study drug.
4. Subjects who have used any investigational agents within 28 days or 5 half-lives from study initiation, whichever is shorter.
5. Subjects who have increasing corticosteroid requirement or a dose >6 mg per day of dexamethasone or equivalent dose of other corticosteroids within 7 days prior to study initiation.
6. Subjects who received radiation therapy within 4 weeks prior to enrollment, unless there is surgical confirmation of recurrent disease or evidence of new enhancing recurrent disease outside of the prior radiotherapy treatment field.
7. Subjects who have had major surgery within 28 days prior to registration.
8. Subjects with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to GT-220F.
9. Subjects with known human immunodeficiency virus or acquired immunodeficiency syndrome-related illness.
10. Subjects with any of the following within 6 months prior to initiation of study drug: uncontrolled congestive heart failure (New York Heart Association Classification 3 or 4), angina, myocardial infarction, cerebrovascular accident, coronary/peripheral artery bypass graft surgery, transient ischemic attack.
11. Pulmonary embolism within 1 month prior to initiation of study drug.
12. Unstable cardiac dysrhythmias or persistent prolongation of the QTc (Fridericia) interval to >470msec.
13. Evidence of Grade ≥ 2 intracranial hemorrhage.
14. Subjects with any severe, acute, or chronic medical or psychiatric condition, or laboratory abnormality that may increase the risk associated with study participation or study drug administration, may interfere with the informed consent process and/or with compliance with the requirements of the study, or may interfere with the interpretation of study results and, in the Investigator's opinion, would make the subject inappropriate for entry into this study.
15. Subjects with uncontrolled intercurrent illness, including active or clinically unstable bacterial, viral or fungal infection requiring systemic therapy.
16. Subjects with difficulty swallowing/unable to swallow pills; malabsorption syndrome; refractory nausea and vomiting, chronic gastrointestinal (GI) disease or previous significant bowel resection with clinically significant sequelae that would preclude adequate absorption of study drug.
17. Another cancer for which they are receiving active treatment.