This phase II Expanded Lung-MAP treatment trial compares how well sacituzumab govitecan alone, ivonescimab alone, or sacituzumab govitecan in combination with ivonescimab works in treating patients with non-small cell lung cancer (NSCLC) that has come back after a period of improvement (recurrent) or is stage IV and has a change in at least 1 of these genes: ALK, EGFR, HER2 (ERBB2), MET, NTRK, RET, and ROS1. This type of gene change is called an actionable genomic alteration (AGA), which means certain treatments can target the change to fight the cancer. Sacituzumab govitecan is a monoclonal antibody, called sacituzumab, linked to a toxic drug called SN-38. Sacituzumab govitecan is a form of targeted therapy because it attaches to specific molecules (receptors) on the surface of tumor cells, known as TROP2 receptors, and delivers SN-38 to kill them. Ivonescimab is a bispecific antibody that can bind to two different antigens at the same time. It binds to programmed cell death protein 1 (PD1), a protein found on the surface of T cells (a type of white blood cell) and vascular endothelial growth factor (VEGF), a protein found on the surface of tumor cells. Ivonescimab may strengthen the immune system and interfere with the ability of tumor cells to grow and spread. Giving a combination of sacituzumab govitecan and ivonescimab work better than either drug alone, and sacituzumab govitecan alone, ivonescimab alone, or sacituzumab govitecan and ivonescimab together may work better than standard treatments at shrinking NSCLC with an AGA.