Docetaxel and SX-682 in Recurrent/Metastatic Head and Neck Squamous Cell Carcinoma, Salivary Gland Carcinoma, and Advanced Prostate Cancer

Background * Recurrent and advanced head and neck squamous cell cancers (HNSCC) are treated with systemic chemotherapy plus or minus checkpoint blockade and overall survival ranges between 6 to 15 months. Recurrent/metastatic salivary gland carcinomas (SGC) lack standardized treatment and respond poorly to checkpoint inhibitors. Therefore, both are clear unmet clinical needs. * Docetaxel (DTX) has demonstrated activity in HNSCC and SGC. Preclinical data suggest that DTX increases both innate and adaptive immunity. Increased objective response rate from DTX was seen in patients with HNSCC previously exposed to checkpoint blockade compared to checkpoint-inhibitors na(SqrRoot) ve patients. * Myeloid-derived suppressor cells (MDSCs) promote an immunosuppressive tumor microenvironment and treatment resistance in HNSCC. Preclinical models of head and neck cancers (HNC) show significant neutrophilic-MDSCs infiltrating the tumor, likely recruited through the CXCR1-2 pathway. MDSCs have been described also in some SGC subtypes, associated with lack of immune infiltration. * In preclinical HNSCC models, blockade of CXCR1-2 chemokine receptors by dual allosteric inhibitor SX-682 has demonstrated a marked reduction in MDSCs trafficking to tumors resulting in increased immune effector cell infiltration. Further, SX-682 appears to downregulate tubulin-beta 3, which is reported to be responsible for DTX resistance. * DTX is a standard option in the treatment of metastatic castrate-resistant prostate cancer (mCRPC). Despite improvements in survival with DTX, nearly all patients treated with DTX become refractory due to the development of resistance. Rationale combinations with DTX are needed to improve upon current treatments and overcome resistance mechanisms. * In mCRPC, MDSCs remain a major mediator of immunosuppression in the tumor microenvironment. Targeting the CXCR1/2 pathway can be an alternate immunotherapeutic approach in treatment in an otherwise immunosuppressive tumor microenvironment. * As in head and neck cancer (HNC), in prostate cancer models, SX-682 appears to downregulate tubulin-beta 3, which is reported to be responsible for DTX resistance. * DTX in combination with SX-682 is a rational combinational approach for treating HNSCC, SGC, and mCRPC offering potential synergistic activity and the induction/restoration of chemotherapy-sensitivity and immune effector activity. Objectives * Phase I: To determine the recommended phase II dose (RP2D) of SX-682 in combination with DTX in participants with HNSCC, SGC, or mCRPC * Phase II: To determine the efficacy of the combination of SX-682 and DTX in participants with HNSCC or SGC using objective response rate (ORR) per response evaluation criteria in solid tumors (RECIST) v 1.1 or in participants with mCRPC using RECIST v1.1 and Prostate Cancer Working Group 3. Eligibility * Age \>= 18 years * Histologically confirmed HNSCC (including oral cavity, oropharynx, larynx, hypopharynx, paranasal sinuses, nasopharynx) or SGC (including adenoid cystic carcinoma \[ACC\] and non-ACC) and recurrent, metastatic (R/M) or advanced incurable disease or mCRPC * Participants with HNSCC or SGC should have received at least 1 standard systemic therapy, or cannot tolerate standard therapy, or there is no standard therapy for their tumor type. * Participants with mCRPC should have received modern anti-androgens. Design * This is a non-randomized, Phase I/II trial to determine the safety and efficacy of DTX in combination with SX-682 in participants with HNSCC, SGC, and mCRPC. * In the Phase I portion of the study, participants will be enrolled in a 3+3 dose escalation schema using 4 SX-682 dose levels and a fixed dose of DTX (Arm 1). * Following identification of RP2D for SX-682, an expansion phase (Phase II) will be initiated, using RP2D SX-682 with a fixed dose of DTX (Arm 2). * DTX will be administered intravenously (IV) on day 8 of each 3-week cycle. * SX-682 will be administered orally twice a day from day 1 to day 11 of each 3-week cycle. * Participants will receive DTX and SX-682 for up to 6 cycles or until disease progression, intolerable side effects, the participant s request to discontinue therapy, or PI decision.