This phase I/II trial tests the safety and efficacy of split-course adaptive radiation therapy in combination with immunotherapy with or without chemotherapy for the treatment of patients with stage IV lung cancer or lung cancer that that has spread to nearby tissue or lymph nodes (locally advanced). Radiation therapy is a standard cancer treatment that uses high energy rays to kill cancer cells and shrink tumors. Split-course adaptive radiation therapy uses patient disease response to alter the intensity of the radiation therapy. Immunotherapy with monoclonal antibodies such as pembrolizumab, ipilimumab or nivolumab may help the body's immune system attack the cancer, and may interfere with the ability of tumor cells to grow and spread. Chemotherapy drugs like carboplatin, pemetrexed, and paclitaxel work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Giving split-course adaptive radiation therapy with standard treatments like immunotherapy and chemotherapy may be more effective at treating stage IV or locally advanced lung cancer than giving them alone.

This is an umbrella study evaluating the efficacy and safety of multiple treatment
combinations in participants with metastatic or inoperable locally advanced breast cancer.

The study will be performed in two stages. During Stage 1, four cohorts will be enrolled in
parallel in this study:

Cohort 1 will consist of Programmed death-ligand 1 (PD-L1)-positive participants who have
received no prior systemic therapy for metastatic or inoperable locally advanced
triple-negative breast cancer (TNBC) (first-line [1L] PD-L1+ cohort).

Cohort 2 will consist of participants who had disease progression during or following 1L
treatment with chemotherapy for metastatic or inoperable locally-advanced TNBC and have not
received cancer immunotherapy (CIT) (second-line [2L] CIT-naive cohort).

Cohort 3 will consist of participants with locally-advanced or metastatic HR+, HER2-negative
disease with PIK3CA mutation who may or may not have had disease progression during or
following previous lines of treatment for metastatic disease (HR+cohort).

Cohort 4 will consist of participants with locally-advanced or metastatic HER2+ /HER2-low
disease with PIK3CA mutation who had disease progression on standard-of-care therapies (HER2+
/HER2-low cohort).

In each cohort, eligible participants will initially be assigned to one of several treatment
arms (Stage 1). In addition, participants in the 2L CIT-nave cohort who experience disease
progression, loss of clinical benefit, or unacceptable toxicity during Stage 1 may be
eligible to continue treatment with a different treatment combination (Stage 2), provided
Stage 2 is open for enrollment.