Inclusion Criteria:

• Patients must provide informed written consent
• Eastern Cooperative Oncology Group (ECOG) performance status 0-1
• Clinical stage IV invasive mammary carcinoma
• For phase 1b: HER2 negative, as defined for phase II; any ER/PR (negative or positive) can be enrolled in the phase 1b portion
• For phase II: ER negative (defined as expression of ER in =< 1% cells), PR negative (defined as expression of PR in =< 1% cells), HER2 negative (acceptable methods of HER2 analysis include IHC [0, 1+], fluorescence in situ hybridization [FISH] with HER2/centromere on chromosome 17 [CEN17] ratio < 2, and/or chromogenic in situ hybridization [CISH] with HER2/CEN-17 ratio < 2), as previously documented by histological analysis
• Androgen receptor positivity, defined as >= 10% of tumor cell nuclei with immunoreactivity for AR on central review at Vanderbilt
• Measurable or bone-only evaluable disease; measurable disease is defined as at least one lesion that can be accurately measured in at least one dimension by Response Evaluation Criteria in Solid Tumors (RECIST) criteria 1.1, with radiologic scans within 21 days of day 1, cycle 1
• Any number of prior therapies as long as patients have adequate performance status and meet all other eligibility criteria
• Prior treatment with anti-androgens other than enzalutamide is acceptable
• Phase 1b only: Formalin-fixed paraffin embedded blocks (FFPB) or fresh frozen tissue from the original diagnosis or the metastatic setting should be located; tissue must be submitted with 3 weeks of study initiation
• Phase II only: Biopsy of a metastatic lesion in patients with reasonably accessible metastatic lesions (chest wall, skin, subcutaneous tissue, lymph nodes, skin, breast, bones, lung, and liver metastases); if a reasonably accessible metastatic lesion is not available, the patient may go on study provided that archived tissue is available; however, if a reasonably accessible site is available for biopsy, the patient must agree to biopsy; any patients not undergoing biopsy must be approved for study enrollment by the Protocol Chair; biopsies may be done with local anesthesia or intravenous conscious sedation, according to institutional guidelines; if a biopsy requires general anesthesia, then it is only allowed if acquisition of tissue is clinically indicated, and excess tissue may be collected for research purposes; patients without sites available for biopsy must have available tissue (archived formalin-fixed paraffin embedded blocks [FFPB] or fresh frozen tissue from original diagnosis or metastatic setting) for correlative studies; tissue needs to be located and available at the time of registration (tissue needs to be submitted within 3 weeks of study initiation)
• Patients must have adequate hematologic, hepatic, and renal function. All tests must be obtained within 28 days of starting treatment. Labs are to be repeated on C1D1 and must still meet eligibility. These include:
• Absolute neutrophil count (ANC) >= 1500/mm^3
• Platelet count >= 75,000/mm^3
• Hemoglobin (HgB) >= 9 g/dL
• Creatinine =< 1.5 X upper limits of normal (ULN)
• INR ≤2
• Total serum bilirubin =< 1.5 x ULN (in patients with known Gilbert syndrome, a total bilirubin =< 3.0 x ULN, with direct bilirubin =< 1.5 x ULN)
• Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =< 3 x ULN (or =< 5.0 x ULN if hepatic metastases are present)
• For patients without known type II diabetes, the following is required at screening:
  • Fasting plasma glucose =< 160 mg/dL (7.49 mmol/L) and glycosylated hemoglobin (HbA1c) < 7.5 % or International Federation of Clinical Chemistry (IFCC) < 53 mmol/mol
• For patients with type II diabetes receiving only oral anti-hyperglycemic therapy (patients receiving insulin are not eligible), the following are required at screening:
  • HbA1c < 8.5 % or IFCC < 69.4 mmol/mol
  • Stable regimen of oral anti-hyperglycemic therapy without insulin usage for at least 3 weeks prior to first study treatment
  • Fasting plasma glucose levels =< 160 mg/dL (8.88 mmol/L) and no hypoglycemia (blood sugar [BS] < 60) during home monitoring for at least 1 week prior to study entry
• Patients must be able to swallow and retain oral medication
• For patients who are not postmenopausal or surgically sterile (absence of ovaries and/or uterus), agreement to remain abstinent or to use two adequate methods of contraception (e.g., condoms, diaphragm, vasectomy/vasectomized partner, tubal ligation), during the treatment period and for at least 30 days after the last dose of study treatment or 3 months after discontinuation of taselisib and/or enzalutamide, whichever is longer; hormone based oral contraceptives are not allowed on study; postmenopausal is defined as:
  • Age >= 60 years
  • Age =< 60 years and amenorrheic for 12 months in the absence of chemotherapy, tamoxifen, toremifene, or ovarian suppression; or follicle stimulating hormone and estradiol in the postmenopausal range
• Patients may have received radiation therapy to painful bone metastases or areas of impending bone fracture as long as radiation therapy is completed >= 2 weeks prior to day 1 of cycle 1 of treatment; patients who have received prior radiotherapy must have recovered from toxicity (=< grade 1) induced by this treatment; baseline radiologic scans must be obtained after completion of radiation
• Patients must complete all screening assessments

Exclusion Criteria:

• Any kind of malabsorption syndrome significantly affecting gastrointestinal function, including history of Crohn's disease or inflammatory bowel disease
• Concurrent anti-cancer therapy (chemotherapy, radiation therapy, surgery, immunotherapy, hormonal therapy, biologic therapy) other than the ones specified in the protocol; patients must have discontinued the above cancer therapies for 1 week prior to the first dose of study medication, as well as recovered to baseline from toxicity induced by previous treatments; any investigational drugs should be discontinued 2 weeks prior to the first dose of study medication and radiotherapy must have been completed >= 2 weeks prior to initiation of study drug (cycle 1, day 1)
• Prior use of PI3K or Akt inhibitors in the metastatic setting for the treatment of cancer; these include, but are not limited to: taselisib, GDC-0941, GDC-0980, BEZ235, BKM120, LY294002, PIK-75, TGX-221, XL147, XL765, SF1126, PX-866, D-87503, D-106669, GSK615, CAL101; patients who have received PI3K/Akt inhibitors previously for < 4 weeks will be eligible
• Prior treatment with enzalutamide
• Current or previously treated brain metastasis or active leptomeningeal disease; head imaging is required during screening in all patients to exclude the presence of central nervous system (CNS) metastatic disease
• History of seizure or any condition that may predispose to seizure; history of loss of consciousness or transient ischemic attack within 12 months before day 1
• Pregnant or lactating women
• Insulin-dependent diabetes; patients with type II diabetes must meet the inclusion criteria outlined above
• Uncontrolled intercurrent illness including, but not limited to:
  • Ongoing or active infection requiring parenteral antibiotics
  • Impairment of lung function (chronic obstructive pulmonary disease [COPD] > grade 2, lung conditions requiring oxygen therapy) or current dyspnea at rest
  • Symptomatic congestive heart failure (class III or IV of the New York Heart Association classification for heart disease)
  • Known left ventricular ejection fraction (LVEF) < 50%
  • Unstable angina pectoris, angioplasty, stenting, or myocardial infarction within 6 months
  • Uncontrolled hypertension (systolic blood pressure > 160 mm Hg or diastolic blood pressure > 100 mm Hg, found on two consecutive measurements separated by a 1 or 2-week period despite adequate medical support)
  • Clinically significant cardiac arrhythmia (multifocal premature ventricular contractions, bigeminy, trigeminy, ventricular tachycardia that is symptomatic or requires treatment [National Cancer Institute-Common Terminology Criteria for Adverse Events, version 4.0, grade 3])
  • Corrected QT using the Fridericia correction formula (QTcF) >= 480 msec on screening electrocardiogram (EKG)
  • Known history of QT/correct QT (QTc) prolongation or Torsades de Pointes (TdP)
  • ST depression or elevation of >= 1.5 mm in 2 or more leads
  • Diarrhea of any cause >= Common Terminology Criteria for Adverse Events (CTCAE) grade 2
  • Active autoimmune disease that is not controlled by nonsteroidal or steroidal (< 10 mg of prednisone per day) anti-inflammatory drugs or active inflammatory disease, including small or large intestine inflammation such as active Crohn's disease or ulcerative colitis, which requires immunosuppressive therapy
  • Psychiatric illness/social situations that would compromise patient safety or limit compliance with study requirements including maintenance of a compliance/pill diary
  • Known history of chronic liver disease including cirrhosis, current alcohol abuse, or infection with hepatitis B virus or hepatitis C virus (active or carrier) or renal failure
  • Known history of chronic pancreatitis
  • Conditions that affect lymphocyte counts, such as human immunodeficiency virus (HIV) infection or immunosuppressive therapy
• Use of prohibited drugs