Phase 1a/1b Study of TPST-1495 as a Single Agent and in Combination With Pembrolizumab in Subjects With Solid Tumors

Subjects must meet all the following inclusion criteria to be eligible: 1. Subjects must have a histologically-confirmed malignancy that is metastatic or unresectable for which there is no remaining standard therapy known to confer clinical benefit. While all solid tumor types are eligible for the dose-escalation and dose-finding portions of the study, there is a preference to enroll patients with colorectal cancer, squamous cell carcinoma of the head and neck, urothelial cancer, endometrial cancer, NSCLC, and gastric or gastroesophageal junction adenocarcinoma. The expansion cohorts are limited to the following tumor types: endometrial, SCCHN, CRC, and tumors with an activating mutation in PIK3Ca. 2. Subjects must have a tumor that is at least 1 cm in a single dimension and is radiographically apparent on CT or MRI. 3. Eastern Cooperative Oncology Group performance status of 0 or 1 at treatment initiation. 4. Life expectancy estimated to be ≥ 12 weeks 5. Adequate organ and marrow function (subjects must not have received transfusions or growth factor support within 1 month prior to first dose of investigational product) as defined below: * Albumin ≥ 3.0 g/dL * Hemoglobin ≥ 10.0 g/dL * Absolute neutrophil count ≥ 1,000/mm3 * Platelet count ≥ 100,000/mm3 * Bilirubin ≤ 1.5 × institutional upper limit of normal (ULN); for subjects with documented/suspected Gilbert's disease, bilirubin should be ≤ 2 × ULN. * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 2.5 × ULN; for subjects with liver metastases, AST or ALT ≤ 5 × ULN * Creatinine ≤ 1.5×ULN OR calculated creatinine clearance (CrCl) ≥ 60 mL/min for subjects with creatinine levels \> 1.5× ULN. Subjects who meet any of the following exclusion criteria will not be eligible to receive investigational product: 1. Concurrent enrollment in another clinical study, unless it is an observational (non interventional) clinical study, a specimen-collection study or the follow-up period of an interventional study. 2. Received more than 4 doses of nonsteroidal anti-inflammatory drugs or COX-2 inhibitors within 2 weeks prior to study treatment initiation. 3. History of allergy or hypersensitivity, GI bleed, or ulceration secondary to nonsteroidal anti-inflammatory drugs or COX-2 inhibitors. 4. History of GI ulcer within 1 year of treatment initiation or history of untreated helicobacter pylori infection. Subjects with history of treated helicobacter pylori infection with confirmation of eradication are eligible 5. History of diverticulitis or any GI bleed within 2 years of treatment initiation. 6. Receipt of any anticancer therapy within the following windows: * Small molecule tyrosine kinase inhibitor (TKI) therapy (including investigational) within 2 weeks or 5 half-lives prior to treatment initiation, whichever is longer * Any type of anti-cancer antibody or cytotoxic chemotherapy within 4 weeks prior to treatment initiation * Radiation therapy for bone metastasis within 2 weeks, any other external radiation therapy within 4 weeks before treatment initiation. Patients with clinically relevant ongoing complications from prior radiation therapy are not eligible * Other investigational therapy within 2 weeks or 5 half-lives prior to dosing, whichever is longer 7. Subjects with active or untreated central nervous system (CNS) metastases 8. New York Heart Association Classification II, III or IV. 9. Baseline QTcF \> 470 milliseconds 10. Receipt of live attenuated vaccines within 30 days prior to the first dose of investigational product. (Killed virus or other non-live vaccines are allowed (including most seasonal influenza vaccines, streptococcus pneumonia vaccines, and newly approved COVID-19 vaccines). 11. Active autoimmune disease or inflammatory disorders including inflammatory bowel disease (e.g., ulcerative colitis or Crohn's disease) requiring systemic treatment (i.e., with use of disease modifying agents, systemic corticosteroids or immunosuppressive drug) within 2 years prior to treatment initiation. 12. Known human immunodeficiency virus (HIV) infection, active Hepatitis B (HBV), or hepatitis C (HCV). Active HBV is defined as a known positive HBsAg result. Active HCV is defined by a known positive HCV antibody result and known quantitative HCV RNA results greater than the lower limits of detection of the assay. Patients receiving antiviral therapy for Hepatitis B or C also are not eligible 13. Uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations including a history of substance abuse that would limit compliance with study requirement, substantially increase risk of incurring AEs or compromise the ability of the patient to give written informed consent. 14. Subjects who are receiving anti-coagulant therapy or who are considered to be at increased risk of bleeding (i.e bleeding disorder or coagulopathy).