Fulvestrant and Palbociclib With or Without Copanlisib in Treating Patients With Hormone Receptor Positive, HER2 Negative, Stage IV Breast Cancer

PRIMARY OBJECTIVES: I. To evaluate the safety profile of fulvestrant + palbociclib + copanlisib (FPC) and determine the recommended phase II treatment dose (RPTD). II. To determine if FPC is superior to fulvestrant + palbociclib (FP) using progression-free survival (PFS) as an endpoint. SECONDARY OBJECTIVES: I. To assess the objective response rate (ORR = partial response \[PR\] + complete response \[CR\]) and clinical benefit rate (CBR = PR + CR + stable disease \[SD\] \>= 6 months) of FPC versus (vs.) FP. II. To compare the median PFS between FPC and FP arms in the following subgroups: tumor PIK3CA/PTEN altered (PIK3CA mutation or PTEN mutation/PTEN loss) and tumor PIK3CA/PTEN not altered (wild type PIK3CA and PTEN and without PTEN loss). TERTIARY OBJECTIVES: I. To evaluate copanlisib pharmacokinetics (PK) when administered in combination with FP. II. To assess the median PFS in the following molecularly defined subgroups treated with either FPC or FP: tumor PIK3CA mutation vs. not, tumor PTEN mutation/PTEN loss vs. not, circulating tumor (ct) deoxyribonucleic acid (DNA) PIK3CA mutation vs. not, ctDNA PI3K/PTEN mutation vs. not, and ctDNA ESR1 mutation vs. not. III. To evaluate ctDNA mutations at baseline and over time for response predictors at baseline, and clonal evolution associated with treatment. IV. To assess resistance mechanisms to FP and FPC at baseline and at disease progression. V. To examine the molecular effects of FP and FPC on tumor and circulating markers. OUTLINE: Patients are randomized to 1 of 2 arms. ARM I: Patients receive fulvestrant intramuscularly (IM) on days 1 and 15 of course 1 and day 1 of subsequent courses, palbociclib orally (PO) on days 1-21, and copanlisib intravenously (IV) over 1 hour on days 1, 8, and 15. Courses repeat every 28 days in absence of disease progression or unacceptable toxicity. ARM II: Patients receive fulvestrant IM on days 1 and 15 of course 1 and day 1 of subsequent courses and palbociclib PO on days 1-21. Courses repeat every 28 days in absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months for 5 years.