Pembrolizumab and ADG106 in Advanced Solid Cancers and Triple Negative Breast Cancer

Inclusion Criteria: * 21 years and above of age * Estimated life expectancy of at least 12 weeks. * Has recovered from acute toxicities from prior anti-cancer therapies. * Has a tumor lesion that can be safely biopsied and who is willing to undergo tumor biopsy at baseline before starting study treatment * Phase Ib * Patients with histologically or cytologically confirmed advanced or metastatic solid tumors who have radiological evidence of progressive disease on study entry * There is no upper limit on the number of prior treatments provided all inclusion/ exclusion criteria are met. * Prior treatment with immunotherapy is allowed. * Phase II * Patients with histologically or cytologically confirmed TNBC, defined by expression of estrogen (ER) and progesterone receptors (PR) of \<1% and HER2 IHC score of 0 or 1+ or HER2 IHC score of 2+ but HER2 FISH negative. * Received at least 1 line but no more than 2 prior lines of systemic therapy in the metastatic setting, including chemotherapy or targeted therapy (e.g., PARP inhibitors). * Tumor CPS≥1 determined by the DAKO 22C3 assay assessed by local or central laboratory. * Measurable disease by RECIST 1.1 criteria as determined by local radiological review. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-1. * Adequate bone marrow function and organ function within 2 weeks of study treatment. * Adequate hematologic function defined as: * Absolute neutrophil count (ANC) - 1.5 x 109/L * Platelets - 100 x 109/L * Hemoglobin - 9 x 109/L * Adequate hepatic function defined as: * Bilirubin ≤1.5 times the upper limit of normal (ULN) * ALT or AST ≤ 2.5 times ULN (or ≤5 times ULN with presence of liver metastases) * Adequate renal function defined as: \- Calculated creatinine clearance of ≥ 60 mL/min, calculated using the formula of Cockroft and Gault: (140-Age) x Mass (kg)/(72 x creatinine mg/dL); multiply by 0.85 if female. * Adequate coagulation function as defined by: * International normalised ratio (INR) OR prothrombin time (PT)/activated partial thromboplastin time (aPTT) ≤1.5x ULN unless participant is receiving anticoagulant therapy, for which it will be acceptable as long as PT or aPTT is within therapeutic range of intended use of anticoagulants. * Patients with reproductive potential must use an approved contraceptive method as detailed in appendix A of the protocol during the period and for at least 120 days (corresponding to 5 terminal half-lives for pembrolizumab therapy) plus 30 days (corresponding to a menstruation cycle) for female, and for at least 120 days plus 90 days (corresponding to a spermatogenesis cycle) for male patients. In addition, females with childbearing potential must have a negative serum pregnancy test within 72 hours prior to study enrolment. * Have signed informed consent in accordance with local institutional guidelines, and able to comply with scheduled visits, treatment plan and study related procedures. Exclusion Criteria: * Patients will be excluded from the study for any of the following reasons: * Treatment within the last 30 days with any investigational drug. Participants must have recovered from all adverse events due to previous therapies to ≤grade 1 or baseline. Participants with ≤grade 2 neuropathy may be eligible. Participants with endocrine related AEs of ≤grade 2 requiring treatment or hormone replacement may be eligible. * Prior treatment with immune checkpoint inhibitor in phase II; prior immune checkpoint inhibitors are allowed for phase Ib * Concurrent administration of any other tumor therapy, including cytotoxic chemotherapy, hormonal therapy, and immunotherapy * Major surgery within 28 days of study drug administration * Prior radiotherapy within 2 weeks of start of study intervention. Participants must have recovered from all radiation-related toxicities, not require corticosteroids for radiotherapy-related adverse events, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation lasting ≤2 weeks to a non-CNS site. * Active infection that requires systemic therapy, and that in the opinion of the investigator would compromise the patient's ability to tolerate therapy. * Serious concomitant disorders that would compromise the safety of the patient or compromise the patient's ability to complete the study, at the discretion of the investigator. * Has severe hypersensitivity (≥grade 3) to pembrolizumab and/or any of its excipients. * Active, known or suspected autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiological corticosteroid replacement therapy for adrenal or pituitary insufficiency etc.) is not considered a form of systemic treatment and is allowed. * Subjects with a condition requiring systemic treatment with either corticosteroids (\>10mg daily prednisone equivalent) or other immunosuppressive medications within 14 days of enrolment. Inhaled or topical steroids, and adrenal replacement steroid \>10mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease. * Has received a live vaccine or live-attenuated vaccine within 30 days prior to first dose of study drug. Administration of killed vaccines is allowed. * Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease * Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS). * Active hepatitis B (defined as viral load ≥1000 copies/ml) or HCV (hepatitis C virus) \[positive HCV RNA\]) * Patients with past HBV infection or resolved HBV infection (defined as the presence of hepatitis B core antibody \[HBcAb\] and absence of HBsAg) are eligible. Patients who are known HBV carriers on anti-viral therapy with a viral load of \<1000 copies may be enrolled. HBV DNA must be obtained in these patients prior to enrolment. * Patients positive for HCV antibody are eligible only if PCR is negative for HCV RNA. * Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment. * Second primary malignancy that is clinically detectable at the time of consideration for study enrolment. Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g., breast or cervical carcinoma in situ) that have undergone potentially curative therapy are not excluded. * Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study intervention. * History of significant neurological or mental disorder, including seizures or dementia. * History of allogenic tissue or solid organ transplant. * Unable to comply with study procedures.