A Study to Examine the Safety of Different Doses of BG-68501 Given to Participants With Advanced-Stage Tumors

Part 1 (Dose Escalation) Inclusion Criteria: * Monotherapy Cohorts: Participants with histologically or cytologically confirmed advanced or metastatic solid tumors potentially associated with CDK2 dependency including HR+/HER2- breast cancer, platinum refractory or resistant serous ovarian cancer (PROC), endometrial cancer, and others. Prior available standard-of-care systemic therapies for advanced or metastatic disease are required. The requirements for enrollment into a food effect evaluation cohort are the same as the monotherapy cohorts with the exception that participants with gastric cancer and gastroesophageal adenocarcinoma are excluded. * Combination Cohorts (BG-68501 with fulvestrant with or without BGB-43395): Enrollment is restricted to only participants with HR+/HER2- BC. In regions where approved and available, participants must have received one or more lines of treatment for advanced/metastatic disease as well as prior endocrine therapy and a CDK4/6 inhibitor in either the adjuvant or advanced/metastatic setting. If applicable, the requirements for enrollment into a food effect evaluation cohort are the same as the combination cohorts. Part 1 (Safety Expansion) and Part 2 (Dose Expansion) Inclusion Criteria: * Participants with advanced, non-resectable, or metastatic HR+/HER2- BC or PROC, including fallopian tube or primary peritoneal cancer. * PROC participants must have received: * ≥ 1 line of platinum-containing chemotherapy for advanced disease. * ≤ 4 prior therapeutic regimens in the advanced/metastatic setting. * HR+/HER2- BC: * Participants enrolled in regions where CDK4/6 inhibitors are approved and available must have received ≥ 1 line of therapy including endocrine therapy and a CDK4/6 inhibitor. Participants can have received up to 2 lines of prior cytotoxic chemotherapy or ADC treatments for advanced disease. General Inclusion Criteria: * Female participants with advanced or metastatic HR+/HER2- BC will be required to have ovarian function suppression using gonadotropin hormone-releasing hormone (GnRH) agonists (such as goserelin) or be postmenopausal. * Eastern Cooperative Oncology Group (ECOG) Performance Status ≤ 1. * Adequate organ function. * For dose escalation, participants with advanced solid tumors other than HR+/HER2- BC must have measurable disease per RECIST 1.1. Participants with HR+/HER2- BC with bone-only disease are eligible for dose escalation only. For safety expansion and dose expansion, all participants must have ≥1 measurable lesion per RECIST v 1.1. General Exclusion Criteria: * For all cohorts: Prior therapy selectively targeting CDK2 inhibition. * For triple combination cohorts: Prior therapy targeting CDK2 or selectively targeting CDK4. Prior CDK4/6 inhibitor therapy is permitted and required in local regions where it is approved and available. * Known leptomeningeal disease or uncontrolled, untreated brain metastasis. Participants with a history of treated central nervous system (CNS) metastases may be eligible if they meet additional criteria. * Any malignancy ≤ 3 years before the first dose of study treatment(s) except for the specific cancer under investigation in this study and any locally recurring cancer that has been treated with curative intent (eg, resected basal or squamous cell skin cancer, superficial bladder cancer, treated papillary thyroid carcinoma, or carcinoma in situ of the cervix or breast). * Uncontrolled diabetes. * Infection requiring systemic antibacterial, antifungal, or antiviral therapy antiviral therapy ≤ 28 days before the first dose of study drug(s), or symptomatic COVID-19 infection. * Active hepatitis B infection or active hepatitis C infection. * Any major surgical procedure ≤ 28 days before the first dose of study treatment(s). * Prior allogeneic stem cell transplantation, or organ transplantation. Note: Other protocol defined Inclusion/Exclusion criteria may apply.