Open-Label Study to Evaluate the Safety, Tolerability, PK, and Efficacy of INX-315 in Patients With Advanced Cancer

Inclusion Criteria: 1. Advanced unresectable or metastatic HR+/HER2- BC that has progressed following treatment with a CDK4/6 inhibitor in the adjuvant or advanced/metastatic setting. 2. Advanced/ metastatic platinum-resistant or platinum-refractory high grade serous epithelial ovarian cancer, fallopian tube cancer, or primary peritoneal cancer, with known amplification of CCNE-1 that progressed after standard systemic therapy 3. Advanced or metastatic solid tumor with known amplification of CCNE-1 that has progressed after standard therapy, been intolerant to or is ineligible for standard therapy 4. At least one measurable lesion as defined by RECIST v1.1 that has not previously been irradiated 5. ECOG performance status score of 0 or 1. 6. Adequate organ function as demonstrated by the following laboratory values: 1. Hemoglobin ≥ 9.0 g/dL 2. Absolute neutrophil count (ANC) ≥ 1.5 × 10\^9/L 3. Platelet count ≥ 100 × 10\^9/L 4. Estimated glomerular filtration rate (eGFR) of ≥60 mL/min 5. Part A and B: Total bilirubin ≤ 1.5 × ULN; AST and ALT ≤ 2.5 × ULN; ≤ 5 × ULN in the presence of liver metastases Part C: Patients with Gilbert's syndrome with a total bilirubin ≤ 2.0 × ULN and direct bilirubin within normal limits 7. Negative pregnancy test Exclusion Criteria: 1. Have received previous therapy with a CDK2/4/6 inhibitor or CDK2 inhibitor. 2. Have central nervous system (CNS) metastases or spinal cord compression that is associated with progressive neurological symptoms or requires corticosteroids (within 4 weeks of enrollment) to control the CNS disease. 3. Have known intracranial hemorrhage and/or bleeding diatheses. 4. Have visceral crisis, lymphangitic spread, or leptomeningeal carcinomatosis. 5. Have clinically active ongoing interstitial lung disease (ILD) of any etiology, including drug-induced ILD, and radiation pneumonitis within 28 days prior to initiation of study treatment. 6. Resting QTcF \> 470 msec, a history of prolonged QT syndrome or Torsades de pointes, or a familial history of prolonged QT syndrome. 7. Uncontrolled, cardiovascular disease (including hypertension) with or without medication 8. History of other malignancies, except for the following: (1) adequately treated basal or squamous cell carcinoma of the skin; (2) curatively treated a) in situ carcinoma of the uterine cervix, b) prostate cancer, or c) superficial bladder cancer; or (3) other curatively treated solid tumor with no evidence of disease for ≥ 3 years. 9. Known HIV infection, including AIDS-related illness, or have active, uncontrolled infection (viral, bacterial, or fungal), including tuberculosis, hepatitis B virus, hepatitis C virus, or COVID-19 infection (symptoms and a positive test result). 10. Requires treatment with a prohibited medication or herbal remedy that cannot be discontinued at least 2 weeks before the start of study drug administration. 11. Have planned or anticipation of the need for major surgical procedure within 28 days of the first dose of study drug (procedures such as central venous catheter placement, tumor needle biopsy, and feeding tube placement are not considered major surgical procedures). 12. Unwilling or unable to comply with scheduled visits, study drug administration plan, laboratory tests, or other study procedures and study restrictions. 13. Radical radiotherapy within 28 days prior to study entry or palliative radiotherapy within 2 weeks prior to study entry. 14. Systemic anti-cancer therapy within 21 days or at least 5 half-lives, whichever is less, prior to the first dose of the study drug 15. Prior irradiation to \> 25% of the bone marrow 16. Previous high-dose chemotherapy requiring prior stem cell transplant 17. Participation in other studies involving investigational drug(s) within 4 weeks prior to study entry. 18. Known or suspected hypersensitivity to active ingredient/excipients in INX-315 or fulvestrant or abemaciclib. 19. Known difficulty in swallowing or tolerating oral medications, or conditions which would impair absorption of oral medications such as active inflammatory gastrointestinal disease, uncontrolled nausea or vomiting (i.e., CTCAE ≥ Grade 3 despite antiemetic therapy), ongoing gastrointestinal obstruction/motility disorder/active inflammation, malabsorption syndrome, chronic diarrhea, known diverticular disease or previous gastric resection or lap band surgery. 20. Has a serious and/or uncontrolled pre-existing medical condition(s) that, in the judgment of the Investigator or the Sponsor, would preclude participation in this study (for example but not limited to, interstitial lung disease, severe dyspnea at rest or requiring oxygen therapy, history of major surgical resection involving the stomach or small bowel, or preexisting Crohn's disease or ulcerative colitis or a preexisting chronic condition resulting in baseline Grade 2 or higher diarrhea)