A Study to Evaluate the Safety and Tolerability of TOS-358 in Adults With HR+ Breast Cancer and Other Select Solid Tumors

Key Inclusion Criteria * Locally advanced, recurrent, or metastatic, incurable (any number of previous lines of therapy is allowed), histologically or cytologically confirmed; HR +/HER2- breast cancer; squamous cell carcinoma of the head and neck; urothelial cancer; or endometrial cancer with no more than 3 prior lines of therapy for metastatic disease * Willing and able to provide written informed consent for this study * Adults ≥ 18 years old at time of consent * Known PIK3CA mutations or amplifications as determined at a CAP/CLIA-certified or equivalently accredited diagnostic laboratory using a validated test * Measurable disease by RECIST 1.1 * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Life expectancy ≥ 6 months, as determined by the investigator * Adequate bone marrow, liver, and kidney function within 14 days prior to first dose of investigational product * Fasting plasma glucose \<= 140 mg/dL AND hemoglobin A1c (HbA1c) \<= 7.0% * Available archived or fresh tumor tissue sample for detection of PIK3CA mutation by central laboratory test Key Exclusion Criteria * Recent systemic anticancer treatment prior to start of treatment (EXCEPTION: Patients with breast cancer who were receiving a fulvestrant-containing regimen at the time of informed consent may remain on fulvestrant while receiving study treatment) * For non-breast cancer: prior treatment with any PI3K, AKT, or mTOR inhibitor, or any agent whose mechanism of action is to inhibit the PI3K-AKT-mTOR pathway, * Has an established diagnosis of diabetes mellitus type 1 or has uncontrolled diabetes mellitus type 2 requiring antihyperglycemic medication * Known active central nervous system (CNS) metastases.