Atezolizumab and Cobimetinib or Idasanutlin in Participants With Stage IV or Unresectable Recurrent Estrogen Receptor Positive Breast Cancer

PRIMARY OBJECTIVES: I. To determine the safety and tolerability of atezolizumab and idasanutlin in patients with estrogen receptor positive (ER+) metastatic breast cancer (mBC) (Phase I). II. To determine the anti-tumor effect of atezolizumab and cobimetinib or idasanutlin in patients with ER+ mBC (Phase II). SECONDARY OBJECTIVES: I. To determine the anti-tumor duration of effect of atezolizumab and cobimetinib or idasanutlin in patients with ER+ mBC (Phase II). II. To determine the safety and tolerability of atezolizumab and cobimetinib or idasanutlin in patients with ER+ mBC (Phase II). EXPLORATORY OBJECTIVES: I. To evaluate if CD8+ T cells are enhanced in the tumor with either MEK or MDM2 inhibition (Phase II). II. To evaluate if MHC-I/II and/or PD-L1 expression is enhanced with MEK inhibition (Phase II). III. To evaluate if T cell chemotractants (CCL5, CXCL9,10,11,13) are upregulated upon MDM2 antagonism (Phase II). IV. To determine if baseline or changes in PDL1 expression, MHC expression, presence of tumor infiltrating lymphocytes, neoantigen expression/ mutation burden (using ribonucleic acid \[RNA\]-and whole exome sequencing), CCL5, CXCL9, CXCL10, CXCL11, and CXCL13 correlate with clinical outcome (Phase II). V. To determine if immunological activity of MEK inhibition can be tracked noninvasively using Zr\^89-atezolizumab (Phase II). OUTLINE: This is a phase 1, dose-escalation study of idasanutlin followed by a phase II study. Participants are assigned to 1 of 2 arms. ARM I: Participants with TP53 gene mutation receive atezolizumab intravenously (IV) over 60 minutes starting with day 15 of course 1 and then on days 1 and 15 of subsequent courses, and cobimetinib orally (PO) daily on days 1-21. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. ARM II: Participants without TP53 gene mutation receive atezolizumab IV over 60 minutes starting with day 15 of course 1 and then on days 1 and 15 of subsequent courses, and idasanutlin PO daily on days 1-5. Courses repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, participants are followed for 28 days.