Brigatinib and Binimetinib in Treating Patients With Stage IIIB-IV ALK or ROS1-Rearranged Non-small Cell Lung Cancer

PRIMARY OBJECTIVES: I. To determine the safety and tolerability of brigatinib in combination with binimetinib in stage IIIB or IV anaplastic lymphoma kinase (ALK) or ROS1 rearranged non-small cell lung cancer (NSCLC) and the recommended phase 2 dose. SECONDARY OBJECTIVES: I. To determine preliminary efficacy of brigatinib in combination with binimetinib in any line of treatment. II. To characterize the pharmacokinetic parameters of brigatinib in combination with binimetinib. EXPLORATORY OBJECTIVES: I. To assess circulating tumor deoxyribonucleic acid (DNA) (ctDNA) utility in evaluating treatment response. II. To evaluate the blockade of downstream signaling indicating response or resistance to treatment of immunohistochemistry (IHC) for phosphatidylinositol 3-kinase (PI3K)/Protein kinase B (AKT)/Mitogen-activated protein kinase (MAPK) pathway activity evaluation. OUTLINE: This a dose-escalation study. Patients receive brigatinib orally (PO) once daily (QD) and binimetinib PO twice daily (BID) on days 1-28. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up for 30 days and then every 6 months for 12 months.