Testing the Use of Ado-Trastuzumab Emtansine Compared to the Usual Treatment (Chemotherapy With Docetaxel Plus Trastuzumab) or Trastuzumab Deruxtecan for Recurrent, Metastatic, or Unresectable HER2-Expressing Salivary Gland Cancers

PRIMARY OBJECTIVES: I. To determine if trastuzumab emtansine (ado-trastuzumab emtansine \[T-DM1\]) shows better progression-free survival (PFS) when compared to docetaxel plus trastuzumab (TH) in recurrent and/or metastatic (R/M) HER2-positive salivary gland cancer (SGC) patients who have not previously received HER2 therapy for unresectable or recurrent and/or metastatic disease, as determined by local assessment. (HER2-Positive Cohort) II. To determine the overall response rate (ORR) by Response Evaluation Criteria in Solid Tumors (RECIST) version (v)1.1 criteria with DS-8201a (trastuzumab deruxtecan) in R/M HER2-low expressing SGC patients. (HER2-Low Expressing Cohort) SECONDARY OBJECTIVES: I. To compare the overall response rate (ORR) by RECIST v1.1 criteria between arms. (HER2-Positive Cohort) II. To compare overall survival (OS) between arms. (HER2-Positive Cohort) III. To compare toxicity using Common Terminology Criteria for Adverse Events (CTCAE) v5.0 criteria between arms. (HER2-Positive Cohort) IV. To assess patient-reported toxicity, as measured by the patient reported outcome (PRO)-CTCAE, between arms, and explore patient-reported symptomatic adverse events (AEs) for tolerability of each treatment arm as measured by the PRO-CTCAE. (HER2-Positive Cohort) V. To assess PFS with DS-8201a (trastuzumab deruxtecan) in HER2-low expressing SGC patients. (HER2-Low Expressing Cohort) VI. To assess OS with DS-8201a (trastuzumab deruxtecan) in HER2-low expressing SGC patients. (HER2-Low Expressing Cohort) VII. To evaluate toxicity of DS-8201a (trastuzumab deruxtecan) using CTCAE v5.0. (HER2-Low Expressing Cohort) EXPLORATORY OBJECTIVES: I. To assess the ORR in patients who receive crossover treatment to T-DM1/TH following disease progression on the TH arm/T-DM1 arm. II. To collect blood and tissue specimens for future translational science studies to examine how tumor genetics, HER2 signaling output/expression, HER2 tumoral heterogeneity, and androgen receptor expression/signaling impacts H and T-DM1 efficacy in the HER2-positive cohort and DS-8201a (trastuzumab deruxtecan) efficacy in the HER2-low expressing cohort. OUTLINE: Patients with HER2-positive disease are randomized to 1 of 2 arms. Patients with HER2-low expression disease are assigned to Arm III. ARM I: Patients receive docetaxel intravenously (IV) over 60 minutes on day 1 of each cycle. Treatment repeats every 21 days for up to 6 cycles in the absence of disease progression or unacceptable toxicity. Patients also receive trastuzumab IV over 90 minutes on day 1 of each cycle. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. Patients on Arm I (TH) can cross over to Arm II (T-DM1) after first progression. Patients undergo a computed tomography (CT) scan or magnetic resonance imaging (MRI) and echocardiography (ECHO) or multigated acquisition (MUGA) scan throughout the trial. Patients may also undergo blood sample collection during screening and on study, as well as a biopsy during screening. ARM II: Patients receive trastuzumab emtansine IV over 90 minutes on day 1 of each cycle. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. Patients on Arm II (T-DM1) can cross over to Arm I (TH) after first progression. Patients undergo a CT scan or MRI and ECHO or MUGA scan throughout the trial. Patients may also undergo blood sample collection and during screening and on study, as well as a biopsy during screening. ARM III: Patients receive trastuzumab deruxtecan IV over 30-90 minutes on day 1 of each cycle. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. Patients undergo a CT scan or MRI and ECHO or MUGA scan throughout the trial. Patients may also undergo blood sample collection and during screening and on study, as well as a biopsy during screening. After completion of study treatment, patients are followed up every 3 months for 2 years and then every 6 months for an additional 3-5 years, then annually.