MK2206 in Combination With Anastrozole, Fulvestrant, or Anastrozole and Fulvestrant in Treating Postmenopausal Women With Metastatic Breast Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed invasive breast cancer that is metastatic stage IV or recurrent metastatic (histologic/cytologic confirmation of recurrence preferred, but not required) * Either the primary or the metastatic tumor must be positive for estrogen-receptor (\> 1% tumor cell staining by immunohistochemistry or an Allred score of \>= 3 by immunohistochemistry) * Patient must have measurable or non-measurable lesions (defined by Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.1 criteria) * Note: to be eligible for the FDG PET imaging studies in Phase IA, the presence of measurable lesions of at least 1.5 cm or the presence of bone lesions is required * Patients may have undergone any number of prior lines of chemotherapy or endocrine regimens but must not have a history of disease progression on anastrozole (Phase IA and Phase IB), fulvestrant (Arm C), or both anastrozole and fulvestrant (Arm D) * Phase IA and IB: * Currently being treated with anastrozole with no evidence of disease progression OR * Currently being treated with letrozole or exemestane with no evidence of disease progression and willing to switch to anastrozole for study enrollment OR * Considering switching to anastrozole due to disease progression from the most recent anti-cancer therapy * Arm C: * Currently being treated with fulvestrant with no evidence of disease progression OR * Considering switching to fulvestrant due to disease progression from the most recent anti-cancer therapy * Arm D: * Currently being treated with either anastrozole or fulvestrant with no evidence of disease progression OR * Currently being treated with letrozole or exemestane with no evidence of disease progression and willing to switch to anastrozole for study enrollment * Considering switching to anastrozole or fulvestrant due to disease progression from the most recent anti-cancer therapy * Patients must be postmenopausal women as defined by one of the following: * Women \> 60 years * Women =\< 60 years with spontaneous cessation of menses \> 12 months prior to registration * Women =\< 60 years with cessation of menses of duration \< 12 months or secondary to hysterectomy AND an follicle stimulating hormone (FSH) level in the postmenopausal range according to institutional standards (or \> 34.4 IU/L if institutional range is not available) prior to registration * Women =\< 60 years on hormonal replacement therapy who have discontinued hormonal therapy AND an FSH level in the postmenopausal range according to institutional standards (or \> 34.4 IU/L if institutional range is not available) prior to registration * Status post bilateral surgical oophorectomy * Premenopausal women on a gonadotropin-releasing hormone (GnRH) analog * Patients must have a life expectancy greater than 4 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 (Karnofsky \>= 70%) * Leukocytes \>= 3,000/mcL * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelet count \>= 100,000/mcL * Total bilirubin not above the institutional upper limit of normal * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal * Creatinine not above the institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * If patients have diabetes mellitus, fasting glucose must be =\< 120 mg/dL and hemoglobin (Hb)A1c =\< 8% * Women of childbearing potential must use two forms of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while she is participating in this study, the patient should inform the treating physician immediately * Patients with known brain metastases are eligible if stable (no evidence of local progression) \>= 3 months after local therapy and are off steroid * Patients who are eligible for this study may also be eligible for and participate in National Cancer Institute (NCI) Protocol 9167, titled "Positron Emission Tomography (PET) with 18F-Fluoroestradiol (FES) as a Predictor of Response in Patients with Breast Cancer Scheduled to Be Treated with MK-2206 in Combination with Either an Aromatase Inhibitor or Fulvestrant on NCI Protocol 8762," in which case the FES-PET in Protocol 9167 has to be performed a minimum of 48 hours and a maximum of 30 days before the first dose of MK-2206; in addition, all FES-related side effects must have resolved before the first dose of MK-2206 * Patients must have the ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients may not have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study; patient must have recovered from adverse events due to agents administered more than 4 weeks earlier * Patients may not be receiving any other investigational agents * Patients may not have a history of allergic reactions attributed to compounds of similar chemical or biologic composition to MK-2206 or other agents used in the study * Patients receiving any medications or substances that are strong inhibitors or inducers of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP 450 3A4) are ineligible * Note: one week washout period is required in patients who were previously taking strong inhibitors or inducers of CYP450 3A4; patients who are currently taking moderate inhibitors or inducers of CYP450 3A4 are encouraged to switch to other medications that do not interact with CYP450 3A4 * Patients with diabetes or in risk for hyperglycemia should not be excluded from trials with MK-2206, but the hyperglycemia should be well controlled on oral agents before the patient enters the trial (i.e. HbA1c =\< 8% and fasting glucose =\< 120 mg/dL) * Cardiovascular: baseline QT Fridericia formula (QTcF) \> 450 msec (male) or QTcF \> 470 msec (female) will exclude patients from entry on study * Patients may not have uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or nursing patients are excluded from the study * Patients with known human immunodeficiency virus (HIV) positive status are excluded from this study * Patients may not have had disease progression on anastrozole (Phase IA and Phase IB), fulvestrant (Arm C), both anastrozole and fulvestrant (Arm D) in either the neoadjuvant, adjuvant (defined as disease recurrence identified within 6 months of adjuvant discontinuation), or metastatic setting * Patients may not have had grade 3 or intolerable grade 2 adverse events during run-in aromatase inhibitor (AI) or fulvestrant therapy prior to starting MK-2206 * Patients may not have had prior therapy with an AKT inhibitor