Post-op T-DM1 in HER-2+ Salivary Gland Carcinomas

Inclusion Criteria: * Subject must have histologically or cytologically confirmed, resectable stage II (with positive margins), III, IVA, or IVB locoregionally advanced salivary gland carcinoma (including any histologic subtype), as defined by 2017 American Joint Committee on Cancer (AJCC), 8th edition. * Willing to provide tissue from a diagnostic biopsy or at the time of cancer resection, and blood samples before, during, and after treatment. * HER2 positive disease as defined by any of the following: * Tumor HER2 expression staining intensity of 2 or 3+ by IHC (from either a preoperative biopsy or resection specimen at the time of oncologic surgery) * HER2 amplification as determined by FISH (HER2/CEP 17 ratio greater than or equal to 2.0 or HER2 mean copy number greater than or equal to 4.0) * HER2 or ERBB2 mutated on tumor genomic sequencing assay (see Section 9.1 for permitted HER2 mutations) * Age 18 years or older * ECOG performance status ≤ 1 (Karnofsky ≥ 60%, see Appendix A) * Participant must have normal organ and marrow function as defined below within 14 days prior to study registration: * leukocytes ≥ 3,000/mcL * absolute neutrophil count ≥ 1,000/mcL * hemoglobin ≥ 9.0 g/dL * platelets ≥ 100,000/mcL * total bilirubin ≤ 2.0 g/dL * AST(SGOT)/ALT(SGPT) ≤ 2.5× institutional upper limit of normal * creatinine within normal institutional limits OR * creatinine clearance ≥50 mL/min/1.73 m2 for participants with creatinine levels above instituti…