Talabostat and Pembrolizumab for the Treatment of Advanced Solid Cancers

Inclusion Criteria:

* Patient with a histology or cytology proven solid advanced cancer, which failed or is intolerant of standard therapies known to offer survival benefit unless standard therapies include PD1 or PD-L1 antibodies

  * Lead-in stage: patient with advanced cancers meeting the criteria above with or without prior treatment with PD1/PDL1 antibodies. Patients with prior treatment with PD1/PDL1 antibodies should be relapsed
  * Efficacy stage cohort A: patients with advanced cancers not previously treated with PD1/PDL1 antibodies
  * Efficacy stage cohort B: patients with advanced cancers which have relapsed or progressed with PD1/PDL1 antibodies
* Patient with a life expectancy of more than 3 months, in the opinion of the investigator
* Patient has Eastern Cooperative Oncology Group (ECOG) performance status of 0 2
* Patients \< 18 years of age have to weigh \> 40 kgs
* Patients must have measurable disease by RECIST 1.1 and iRECIST. Disease amenable to a biopsy is not mandatory
* Patient's acute toxic effects of previous anticancer therapy have resolved to =\< grade 1 except for grade 2 peripheral neuropathy or any grade of alopecia
* Serum creatinine =\< 1.5 times institutional upper limit of normal (ULN) or calculated creatinine clearance \> 40 mL/min
* Serum albumin \>= 2.5 g/dL
* Total bilirubin =\< 1.5 x ULN (for patients with known Gilbert syndrome \< 3 x ULN)
* Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 3 x institutional ULN (patients with hepatic metastases must have AST/ALT =\< 5 x ULN)
* Absolute neutrophil count (ANC) \>= 1.0 x 10\^9/L
* Hemoglobin \>= 8 g/dL and no red blood cell transfusions during the prior 7 days
* Platelet count \>= 75 x 10\^9/L
* Women of childbearing potential (WOCBP) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 14 days prior to the initiation of treatment and/or postmenopausal women must be amenorrhoeic for at least 12 months to be considered of non-childbearing potential. Women of childbearing potential must agree and commit to the use of 2 highly effective methods of birth control throughout the duration of the study until at least 4 months following the last dose of study drug. Acceptable methods are defined as those that result, alone or in combination, in a low failure rate (ie, less than 1% per year) when used consistently and correctly, such as surgical sterilization, an intrauterine device, or hormonal contraception in combination with a barrier method. It is currently unknown whether BXCL701 or pembrolizumab may reduce the effectiveness of systemically acting hormonal contraceptives; therefore, women using systemically acting hormonal contraceptives should add a barrier method. In certain countries (if permitted by law), WOCBP may agree to abide by heterosexual sexual abstinence during the time of participation in this study
* Male patients and their female partners of childbearing potential must agree and commit to use a barrier contraception (eg, condom with spermicidal foam/gel/film/cream/suppository) throughout the duration of the study until at least 60 days following the last dose of study drug, in addition to their female partners using either an intrauterine device or hormonal contraception and continuing until at least 4 months days following the last dose of study drug. This criterion may be waived for male patients who have had a vasectomy \> 6 months before signing the informed consent form (ICF)
* Patient has signed informed consent prior to initiation of any study-specific procedures or treatment
* Patient is able to adhere to the study visit schedule and other protocol requirements

Exclusion Criteria:

* Patient cannot swallow oral medication
* Patient is on gliptins
* Patient has active central nervous system (CNS) metastases not controlled by prior surgery or radiotherapy (patient must be off steroids). Patients with signs or symptoms suggestive of brain metastasis are not eligible unless brain metastases are ruled out by brain magnetic resonance imaging/computed tomography (MRI/CT)
* Patient has received external-beam radiation or another systemic anticancer therapy within 14 days or 5 half-lives, whichever is shorter, prior to study treatment
* Patient has received treatment with an investigational systemic anticancer agent within 14 days prior to study drug administration
* Patient has an additional active malignancy that may confound the assessment of the study endpoints. Patients with the following concomitant neoplastic diagnoses are eligible: non-melanoma skin cancer and carcinoma in situ (including transitional cell carcinoma, anal carcinoma, and melanoma in situ). Patients with simultaneous cancers, which are not active and do not require treatment may be eligible contingent on discussion with the principle investigator (PI) and supporter
* Patient has clinically significant cardiovascular disease (e.g., uncontrolled or any New York Heart Association class 3 or 4 congestive heart failure, uncontrolled angina, history of myocardial infarction, unstable angina or stroke within 6 months prior to study entry, uncontrolled hypertension or clinically significant arrhythmias not controlled by medication)
* Patient has a diagnosis of immunodeficiency or is receiving systemic steroid therapy at a prednisone equivalent dose of \> 10 mg daily for at least 1 week or other form of immunosuppressive therapy within 7 days prior to cycle 1 day 1 (C1D1)
* Patient has uncontrolled intercurrent illness including, but not limited to, uncontrolled infection, disseminated intravascular coagulation, or psychiatric illness/social situations that would limit compliance with study requirements
* Patient has known positive status for human immunodeficiency virus active or chronic hepatitis B or hepatitis C. Patients with history of hepatitis B or C and undetectable viral load are eligible. Screening is not required
* Has a clinically significant upper gastrointestinal obstruction, abnormal physiological function or malabsorption syndrome that may affect the absorption of the study medication
* Patient has any medical condition which, in the opinion of the investigator, places the patient at an unacceptably high risk for toxicity
* Patient is pregnant or breast-feeding