This phase II trial studies how well Akt inhibitor MK-2206 (MK-2206) and anastrozole with or without goserelin acetate works in treating patients with stage II-III breast cancer. MK-2206 may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Estrogen can cause the growth of breast cancer cells. Hormone therapy using anastrozole and goserelin acetate may fight breast cancer by blocking the use of estrogen by the tumor cells. Giving MK-2206, anastrozole, and goserelin acetate together may kill more tumor cells.

PRIMARY OBJECTIVES: I. To determine the pathologic complete response (pCR) rate of neoadjuvant MK-2206 (Akt inhibitor MK-2206) in combination with anastrozole (goserelin \[goserelin acetate\] is added if premenopausal) in women with clinical stage II or III phosphatidlinositol-4,5-bisphosphate 3-kinase, catalytic subunit alpha (PIK3CA) mutated estrogen receptor (ER)+/human epidermal growth factor receptor 2 (HER2)- breast cancer. SECONDARY OBJECTIVES: I. To determine the safety profile of neoadjuvant MK-2206 in combination with anastrozole (goserelin is added if premenopausal) in women with clinical stage II or III PIK3CA mutated ER+/HER2- breast cancer. II. To estimate the rate of clinical response and radiologic response using the World Health Organization (WHO) criteria. TERTIARY OBJECTIVES: I. For pre and post-menopausal women separately, to examine serum estradiol levels prior to pre-registration, prior to registration, after 2 cycles of anastrozole plus MK-2206 (cycle 3 day 1) and pre surgery. II. To examine the percent change in the apoptotic index after 2 weeks of combination therapy with MK-2206 and anastrozole (cycle 1 day 17) relative to apoptotic index after 4 weeks of treatment with anastrozole alone (pre MK-2206). III. To examine the change in Ki67 levels after 2 weeks of combination therapy with MK-2206 and anastrozole (cycle 1 day 17) relative to that after 4 weeks of treatment with anastrozole alone (pre MK-2206). IV. To estimate the proportion of patients whose Ki67 values is at most 10% after 2 weeks of combination therapy with MK-2206 and anastrozole (cycle 1 day 17) among those whose Ki67 was more than 10% or more after 4 weeks of treatment with anastrozole alone (pre MK-2206). V. To examine the pharmacodynamic effect of MK-2206 in combination with anastrozole (or anastrozole in combination with goserelin) on PI3K pathway signaling using serially collected tumor specimens. VI. To explore molecular mechanisms which could affect tumor response to combination MK-2206 and anastrozole (or anastrozole in combination with goserelin) in PIK3CA mutant ER+ breast cancer. VII. To examine the PIK3CA mutation status in circulating plasma deoxyribonucleic acid (DNA) prior to and following therapy on serially collected peripheral blood (pre anastrozole, pre MK-2206, cycle 1 day 17, and at the time of surgery) and to correlate with tumor tissue PIK3CA status. VIII. To examine PIK3CA mutation status of the residual cancer collected at the time of surgery post 4 cycles of neoadjuvant MK-2206 and anastrozole. OUTLINE: Patients receive Akt inhibitor MK-2206 orally (PO) on days 2, 9, 16, and 23; anastrozole PO daily on days 1-28; and goserelin acetate subcutaneously (SC) on day 1 (premenopausal patients only). Treatment repeats every 28 days for 4 courses in the absence of disease progression or unacceptable toxicity. Standard of care surgery (breast and axillary lymph node surgery) is performed 1-3 weeks following the last dose of Akt inhibitor MK-2206. After completion of study treatment, patients are followed up for 30-60 days.