Phase I/II Trial Investigating the Safety, Tolerability, Pharmacokinetics, Immune and Clinical Activity of SX-682 in Combination With BinTrafusp Alfa (M7824 or TGF-beta "Trap"/PD-L1) With CV301 TRICOM in Advanced Solid Tumors (STAT)

* INCLUSION CRITERIA: * Participants must have histologically or cytologically confirmed: * Metastatic or locally advanced, Solid tumor (Cohort 1) OR --Metastatic or locally recurrent, non-resectable Triple Negative Breast Cancer (TNBC), defined as estrogen receptor (ER) \< 10%, progesterone receptor (PR) \< 10% per immunohistochemistry (IHC) and human epidermal growth factor receptor 2 (HER2) negative. HER2 negative or unamplified breast cancer is defined as IHC 0 or 1+ or IHC 2+ with FISH average HER2 copy number \< 4.0 signals per cell or HER2/chromosome 17 (CEP17) \< 2.0 with average HER2 copy number \< 4.0 signals per cell.\[89\] HER2 testing must have been performed in a laboratory accredited by the College of American Pathology (CAP) or another accrediting entity (Cohort 2). OR * Metastatic or locally recurrent, non-resectable p16 negative Head and Neck Squamous Cell Cancer (HNSCC). Oropharyngeal tumors must be negative for p16 overexpression by IHC per American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guidelines and in a CAP accredited lab.\[90\] All other head and neck malignancies do not require p16 testing (Cohort 3). * Participants must have histologically or cytologically confirmed metastatic or locally advanced disease. Historical reports from a CAP accredited lab are acceptable. * Subjects in Arms 1 and 2 may have disease that is measurable or non-measurable but evaluable disease (e.g. present on bone scan, rising tumor markers, non-measurable by Response Evaluation Criteria in Solid Tumors (RECIST) but visible on computed tomography (CT) scan). Participants with third space fluid (for example pleural effusions) as only site of disease will not be eligible. Subjects in Arm 3 must have measurable disease according to RECIST 1.1 * Participants must * have received at least one prior systemic therapy for metastatic or locally advanced disease, unless there is no standard treatment available, OR --not tolerate standard first line treatment, OR --decline standard treatment after appropriate counseling has been provided. Note: Participants in Arm 3, Cohort 3 who have programmed death-ligand 1 (PD-L1) positive triple-negative breast cancer (TNBC) must have progressed on atezolizumab + nab-paclitaxel. Participants in Arm 3, Cohort 3 (p16 negative head and neck squamous cell carcinomas (HNSCC) must have progressed on or been intolerant to a regimen involving a platinum drug or cetuximab monotherapy. * Age greater than or equal to 18 years. * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1. * Participants must have adequate organ and marrow function as defined below: * Absolute neutrophil count (ANC) \>1,500/mcL * Platelets \>100,000/mcL * Hemoglobin \> 9 g/dL without a blood transfusion in the 14 days prior to enrollment. * Total bilirubin \< 1.5X upper limit of normal (ULN) OR in subjects with Gilbert s Syndrome, a total bilirubin \< 3.0 x ULN * Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamic-pyruvic aminotransaminase (SGPT) \<2.5 X institutional upper limit of normal OR in subjects with known liver metastasis, AST/ALT \< 3.0 X ULN * An estimated creatinine clearance (CrCl) \> 60 mL/min/1.73 m\^2 using the Cockcroft-Gault calculation (https://www.kidney.org/professionals/KDOQI/gfr\_calculatorCoc). * The effects of immunotherapies on the developing human fetus are unknown. For this reason and because immunotherapy agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) at the time of study entry, for the duration of study treatment and up to 6 months after the last dose of the study drug (s). Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. * Participants with well-controlled human immunodeficiency virus (HIV) infection are eligible for trial as long as: * On an effective anti-retroviral therapy (ART) \> 4 weeks and with evidence of viral suppression defined as HIV viral load \< 400 copies/mL at enrollment * CD4+ count \> 200 cells/microL at enrollment * No reported opportunistic infections within 6 months prior to enrollment except for the following which will be allowed: * Esophageal candidiasis treated within last 6 months or currently improving with antifungal treatment * Oral and/or genital herpes simplex virus (HSV) treated within last 6 months or currently improving with antiviral treatment * Mycobacterium avium infection in last 6 months or that has been treated for at least 1month. * Immunomodulating drugs must be discontinued at least 1 weeks prior to enrollment for recent short course use (less than or equal to 14 days) or discontinued at least 4 weeks prior to enrollment for long term use (\> 14 days). * Participants must have a received their last treatment \> 4 weeks or 5 half-lives of the last treatment drug, whichever is shorter before starting on trial. * Participants with known history of hepatitis B (HBV) infection are eligible for trial as long as the HBV viral load is undetectable. * Patients with known history of hepatitis C (HCV) infection must have been treated and cured (viral load is undetectable). For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable or unquantifiable HCV ribonucleic acid (RNA) 12 weeks or longer after definitive treatment completion. * Subjects must be able to understand and be willing to sign a written informed consent document. EXCLUSION CRITERIA: * Participants who are receiving any other investigational agents. * Participants with active brain metastases or central nervous system metastasis (less than 28 days out from definitive radiotherapy or surgery of brain metastasis) are excluded from this clinical trial. However, patients with treated brain metastasis are eligible if there is no magnetic resonance imaging (MRI) evidence of progression for 6 weeks after treatment is complete and the MRI within 28 days prior to enrollment. Participants requiring immunosuppressive doses of systemic corticosteroids (\> 10 mg/day prednisone equivalent) for palliation are excluded. Patients with evidence of intratumoral or peritumoral brain metastasis hemorrhage on screening imaging are also excluded unless the hemorrhage of brain metastases is grade \< 1 and has been stable on two consecutive imaging scans. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to any of study drugs * Steroid use or active autoimmune disease that might deteriorate when receiving an immunostimulatory agent with the exception of: * Diabetes type I, eczema, vitiligo, alopecia, psoriasis, hypo- or hyperthyroid disease or other mild autoimmune disorder not requiring immunosuppressive treatment; * Participants requiring hormone replacement with corticosteroid are eligible if the steroids are administered only for the purpose of adrenal insufficiency and at doses of \<10 mg of prednisone or equivalent per day; * Administration of steroids for other conditions through a route known to result in a minimal systemic exposure (topical, intranasal, intro-ocular, or inhalation) is acceptable; * Participants on physiologic doses of systemic intravenous or oral corticosteroid therapy (greater than or equal to the equivalent of prednisone 10 mg/day. * The use of corticosteroids as premedication for contrast-enhanced studies which is allowed prior to enrollment. * Participants with a history of serious intercurrent chronic or acute illness, such as cardiac or pulmonary disease, hepatic disease, bleeding diathesis or recent (within 3 months) clinically significant bleeding events or other illness considered by the Investigator as high risk for investigational drug treatment. * History of second malignancy within 3 years of enrollment except for the following: adequately treated localized skin cancer, ductal carcinoma in situ, cervical carcinoma in situ, superficial bladder cancer or other localized malignancy which has been adequately treated. * Receipt of any organ transplantation requiring ongoing immunosuppression including allogenic stem-cell transplant. * Participants with bone metastases who have initiated denosumab or a bisphosphonate therapy within 28 days prior to enrollment. Continuation of prior therapy is allowed. * Participants who have a corrected QT interval by Fridericia (QTcf) interval \> 475 msec or \> 480 msec with a bundle branch block (BBB) on screening electrocardiogram. * Participants with a personal or family history of long-QT syndrome or are on a concomitant drug that is known to cause significant QTc prolongation within 2 weeks or 5 half-lives (whichever is shorter) of enrollment * Participants with heart failure (New York Heart Association \[NYHA\] class III or IV) or cerebrovascular accident within one year or acute myocardial infarction within one year. * Participants unwilling to accept blood products or blood transfusions as medically indicated. As there is a risk of severe bleeding with M7824, participants must be willing to receive blood transfusions if medically necessary for their own safety * Any other condition, which would, in the opinion of the Principal Investigator indicated the subject is a poor candidate for the clinical trial or would jeopardize the subject or the integrity of the data obtained. * Pregnant women are excluded from this study because study drugs potential for teratogenic or abortifacient effects are unknown. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with study drugs, breastfeeding should be discontinued if the mother is treated with study drugs.