Testing Ado-Trastuzumab Emtansine as a Potential Targeted Treatment in Cancers With HER2 Genetic Changes (MATCH-Subprotocol Q)

PRIMARY OBJECTIVE: I. To evaluate the proportion of patients with objective response (OR) to targeted study agent(s) in patients with advanced refractory cancers/lymphomas/multiple myeloma. SECONDARY OBJECTIVES: I. To evaluate the proportion of patients alive and progression free at 6 months of treatment with targeted study agent in patients with advanced refractory cancers/lymphomas/multiple myeloma. II. To evaluate time until death or disease progression. III. To identify potential predictive biomarkers beyond the genomic alteration by which treatment is assigned or resistance mechanisms using additional genomic, ribonucleic acid (RNA), protein and imaging-based assessment platforms. IV. To assess whether radiomic phenotypes obtained from pre-treatment imaging and changes from pre- through post-therapy imaging can predict objective response and progression free survival and to evaluate the association between pre-treatment radiomic phenotypes and targeted gene mutation patterns of tumor biopsy specimens. OUTLINE: Patients receive trastuzumab emtansine intravenously (IV) over 30-90 minutes on day 1. Cycles repeat every 21 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months if less than 2 years from study entry, and then every 6 months for year 3 from study entry.