Testing the Biological Effects of DS-8201a on Patients With Advanced Cancer

Inclusion Criteria: * Patients must have histologically confirmed malignancy that is metastatic or unresectable and for which standard curative or palliative measures do not exist or are no longer effective * Patients must have measurable or evaluable disease * Age \>= 18 years of age * Patients must have HER2-positive or HER2-expressing tumors as defined by Clinical Laboratory Improvement Act (CLIA)-certified labs. Patients must have either: * A tumor HER2 immunohistochemistry (IHC) score of 1+ or greater (as determined by a CLIA-certified IHC test, per criteria specified) or * A tumor with HER2 amplification (as determined by CLIA-certified in situ hybridization \[ISH\] or a CLIA-certified next-generation sequencing assay) * Patients with HER2 mutations are eligible, as are patients with HER2-positive breast cancer * Patients must have Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Absolute neutrophil count \>= 1,500/mcL (within 8 days of enrollment) * Platelets \>= 100,000/mcL (within 8 days of enrollment) * Leukocytes \>= 3,000/mcL (within 8 days of enrollment) * Hemoglobin \>= 9 g/dL (\>= 8.0 g/dL for gastric cancer \[GC\] only) (within 8 days of enrollment) * Serum albumin \>= 2.5 g/dL (GC only) (within 8 days of enrollment) * Total bilirubin =\< 1.5 x institutional upper limit of normal (=\< 3 x upper limit of normal in the presence of documented Gilbert's syndrome or liver metastases at baseline) (within 8 days of enroll…