Testing the Addition of Copanlisib to Usual Treatment (Fulvestrant and Abemaciclib) in Metastatic Breast Cancer

Inclusion Criteria:

* Patients must have histologically or cytologically confirmed ER and/or PR positive, HER2 negative or non-amplified breast cancer that is stage IV, with measurable or non-measurable disease. ER/PR positivity is defined as at least 1% positive or an Allred score of at least 3. HER2 status is defined per the 2018 American Society of Clinical Oncology/College of American Pathologists (ASCO/CAP) guideline
* All patients must agree to provide archival tumor material for research and must agree to undergo research tumor biopsy before treatment if presence of easily accessible lesions (judged by the treating physician). For patients with bone only disease, or patients without easily accessible lesions for the baseline research biopsy, availability of archival tumor material (2 x 4-5 micron section unstained slides, plus 15-20 x 10 micron section unstained slides or a tumor rich block) from previous breast cancer diagnosis or treatment is required for central PTEN and PIK3CA analysis
* No more than 1 prior chemotherapy in the metastatic setting. There is no limit on prior lines of endocrine therapy. (For patients enrolling to the phase 1 portion of the study, prior fulvestrant, CDK4/6 inhibitor, and everolimus is allowed)
* For patients enrolling to the randomized phase 2 portion of this study, demonstrated resistance to prior endocrine therapy in the metastatic setting is required; this is defined as:

  * Progressed on prior endocrine therapy in the metastatic setting or,
  * Relapsed on adjuvant endocrine therapy or,
  * Relapsed within 12 months of completing adjuvant endocrine therapy or,
  * If received adjuvant CDK4/6 inhibitor, relapsed at least 2 years after completion of adjuvant CDK4/6 inhibitor
* Washout from prior systemic anti-cancer therapy of at least 3 weeks from chemotherapy or 5 half-lives from oral targeted drugs, and treatment related adverse events recovered to grade 1 (except for alopecia) before the start of study treatment. Washout from prior radiation therapy of at least 2 weeks before the start of the study treatment. Washout from prior endocrine therapy is not required
* Age \>= 18 years. Because no dosing or adverse event (AE) data are currently available on the use of copanlisib in combination with abemaciclib and fulvestrant in patients \< 18 years of age, and because breast cancer is rare in children, children are excluded from this study
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Leukocytes \>= 3,000/mcL (no more than 7 days before starting study treatment)
* Absolute neutrophil count \>= 1,500/mcL (no more than 7 days before starting study treatment)
* Platelets \>= 100,000/mcL (no more than 7 days before starting study treatment)
* Hemoglobin \>= 8.0 g/dL (no more than 7 days before starting study treatment)
* Total bilirubin =\< 1.5 x institutional upper limit of normal (=\< 3 x institutional upper limit of normal for patients with Gilbert syndrome) (no more than 7 days before starting study treatment)
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x institutional upper limit of normal (=\< 5 x institutional upper limit of normal for patients with liver involvement) (no more than 7 days before starting study treatment)
* Glomerular filtration rate \>= 30 mL/min according to the Modification of Diet in Renal Disease (MDRD) abbreviated formula (no more than 7 days before starting study treatment)
* Lipase =\< 1.5 x upper limit of normal (ULN) (no more than 7 days before starting study treatment)
* International normalized rate (INR) and partial thromboplastin time (PTT) =\< 1.5 x ULN (except those on anti-coagulation therapy) (no more than 7 days before starting study treatment)
* Hemoglobin (Hb)A1c =\< 8.5% or fasting glucose =\< 120 mg/dL on at least 2 occasions within 14 days prior to registration if diabetic (no more than 7 days before starting study treatment)
* Left ventricular ejection fraction (LVEF) \>= 50%
* Patients may be postmenopausal or premenopausal women on or planned to receive gonadotropin-releasing hormone (GnRH) agonist
* The effects of copanlisib on the developing human fetus are unknown. For this reason and because maternal toxicity, developmental toxicity and teratogenic effects have been observed in nonclinical studies and PI3K inhibitors as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 6 months after the last dose of copanlisib. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 6 months after completion of copanlisib administration
* Ability to understand and willing to sign a written informed consent document (or legally authorized representative, if applicable). Patient must agree to research team access to prior breast cancer diagnosis and treatment records, as well as reports of clinical tumor and blood sequencing results
* Patients with a history of treated brain metastases are allowed in the phase I portion of the trial provided there is no disease progression symptomatically and by imaging within 28 days prior to registration AND if the patient is off steroids
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
* Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial

Exclusion Criteria:

* For patients enrolling to the randomized phase 2 portion of the study, prior treatment with a CDK4/6 inhibitor or fulvestrant, or a PI3K inhibitor in the metastatic setting is not allowed
* Patients who have had chemotherapy within 3 weeks or radiotherapy within 2 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study
* Patients who are receiving any other investigational agents
* Immunosuppressive therapy is not allowed while on study
* Receiving anti-arrhythmic therapy (beta blockers or digoxin are permitted)
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to copanlisib, PI3K inhibitors, or other agents used in study
* For the randomized phase 2 portion of the study, patients with brain metastasis or a history of brain metastasis are not eligible

  * For the phase 1 portion of the study, patients with progressive brain metastases should be excluded because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events (AEs)
* Copanlisib is primarily metabolized by CYP3A4. Therefore, the concomitant use of strong inhibitors of CYP3A4 (e.g., ketoconazole, itraconazole, clarithromycin, ritonavir, indinavir, nelfinavir and saquinavir), and strong inducers of CYP3A4 (e.g., rifampin, phenytoin, carbamazepine, phenobarbital, St. John's wort) are not permitted from 14 days prior to enrollment until the end of the study

  * It is important to regularly consult a frequently-updated medical reference for a list of drugs to avoid or minimize use of. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product
* Systemic corticosteroid therapy at a daily dose higher than 15 mg prednisone or equivalent is not permitted while on study. Previous corticosteroid therapy must be stopped or reduced to the allowed dose at least 7 days prior to the computed tomography (CT)/magnetic resonance imaging (MRI) screening. If a patient is on chronic corticosteroid therapy, corticosteroids should be de-escalated to the maximum allowed dose before the screening. Patients may be using topical or inhaled corticosteroids. Short-term (up to 7 days) systemic corticosteroids above 15 mg prednisolone or equivalent will be allowed for the management of acute conditions (e.g., treatment non-infectious pneumonitis)
* Major surgical procedure or significant traumatic injury (as judged by the investigator) within 28 days before start of treatment, or have not recovered from major side effects, open biopsy within 7 days before start of treatment
* Uncontrolled intercurrent illness, including but not limited to, symptomatic congestive heart failure (\> New York Heart Association \[NYHA\] class 2), unstable angina pectoris, new-onset angina, uncontrolled hypertension despite optimal medical management, seizure disorder requiring medication, or psychiatric illness/social situations that would limit compliance with study requirements
* Myocardial infarction \< 6 months before start of treatment
* Arterial or venous thrombotic or embolic events such as cerebrovascular accident (including transient ischemic attacks), deep vein thrombosis or pulmonary embolism within 3 months before the start of study medication
* The patient has a personal history of any of the following conditions: syncope of cardiovascular etiology, ventricular arrhythmia of pathological origin (including, but not limited to, ventricular tachycardia and ventricular fibrillation), or sudden cardiac arrest
* Proteinuria \>= grade 3 as assessed by a 24-hour (h) protein quantification or estimated by urine protein: creatinine ratio \> 3.5 on a random urine sample
* History of bleeding diathesis. Any hemorrhage or bleeding event \>= grade 3 within 4 weeks prior to the start of study medication
* History or concurrent condition of interstitial lung disease of any severity and/or severely impaired lung function
* History of having received an allogeneic bone marrow or organ transplant
* Patients with non-healing wound, ulcer, or bone fracture not due to breast cancer
* Patients with active, clinically serious infections \> grade 2 (Common Terminology Criteria for Adverse Events \[CTCAE\] version \[v\] 5.0)
* Patients with HbA1c \> 8.5% at screening
* Concurrent diagnosis of pheochromocytoma
* Has undergone blood or platelet transfusion \< 7 days prior to start of treatment
* Pregnant women are excluded from this study because copanlisib is a PI3K inhibitor agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with copanlisib, breastfeeding should be discontinued if the mother is treated with copanlisib. These potential risks may also apply to other agents used in this study
* Hepatitis B (HBV) or hepatitis C (HCV). All patients must be screened for HBV and HCV up to 28 days prior to study drug start using the routine hepatitis virus lab panel. Patients positive for hepatitis B surface antigen (HBsAg) and/or hepatitis B core antibody (HBcAb) will be eligible if they are negative for HBV DNA, these patients should receive prophylactic antiviral therapy. Patients positive for anti-HCV antibody will be eligible if they are negative for HCV RNA
* HIV positive patients on combination antiretroviral agents that are strong CYP3A4 inhibitors or inducers and who are unwilling or unable to change to antiretroviral therapies without such interactions are ineligible because of the potential for pharmacokinetic interactions with copanlisib, abemaciclib, and fulvestrant. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated
* Patients with history of, or current autoimmune disease are not eligible
* History of major surgical resection involving the stomach or small bowel, or preexisting Crohn's disease or ulcerative colitis or a preexisting chronic condition resulting in baseline grade 2 or higher diarrhea