Preventing High Blood Sugar in People Being Treated for Metastatic Breast Cancer

Inclusion Criteria:

* Histologically confirmed metastatic HR-positive, HER2-negative breast cancer. HR positive is defined by ER status \>10% immunohistochemical (IHC) staining of any intensity. HER2 negativity is defined as the following as per the 2018 American Society of

Clinical Oncology and College of American Pathologists guidelines:

* IHC score of 0 or 1+ or
* Single-probe average HER2 copy number of \<4 signals/cell or
* Dual-probe HER2/CEP17 ratio \<2 with an average HER2 copy number of \<4 signals/cell or
* IHC 0, 1+, or 2+ and dual-probe HER2/CEP17 ratio ≥2 with an average HER2 copy number of \<4 signals/cell or
* IHC 0 or 1+ and dual-probe HER2/CEP17 ratio \<2 with an average HER2 copy number of ≥6 signals/cell or
* IHC 0 or 1+ and dual-probe HER2/CEP17 ratio \<2 with an average HER2 copy number of ≥4 and \<6 signals/cell.

  * Presence of one or more activating PIK3CA mutations in tumor tissue.
  * Measurable or non-measurable disease per RECIST v1.1 OR at least one predominantly lytic bone lesion must be present.
  * Written informed consent provided
  * Female or male ≥18 years of age
  * Adequate archived tumor tissue for the analysis of PIK3CA mutational status or evaluable circulating tumor DNA (ctDNA) for analysis of PIK3CA mutation status
  * Recurrence or progression of disease during or after endocrine-based therapy
  * Eastern Cooperative Oncology Group performance status of 0 or 1.
  * Life expectancy ≥6 months.
  * Adequate organ and marrow function as defined below:
* Hemoglobin ≥9.0 g/dL (without blood transfusion within 7 days of laboratory test used to determine eligibility)
* Absolute neutrophil count ≥1.5 × 109/L (without granulocyte colony stimulating factor support within 2 weeks of laboratory test used to determine eligibility)
* Platelet count ≥100 × 109/L (without transfusion within 2 weeks of laboratory test used to determine eligibility)
* Total bilirubin (TB) ≤1.0 × institutional upper limit of normal (ULN; Patients with known Gilbert's disease who have TB ≤3 × ULN may be enrolled)
* Aspartate transaminase/alanine transaminase ≤2.5 × ULN with normal alkaline phosphatase (≤5 × ULN for patients with liver metastases) OR ≤1.5 × ULN in conjunction with alkaline phosphatase \>2.5 × ULN
* Creatinine ≤1.5 mg/dL.

  * Fasting blood glucose ≤140 mg/dL and HbA1c \<8% (both criteria have to be met) and not on anti-hyperglycemic medications other than metformin (i.e., metformin is allowable if fasting blood glucose and HbA1c parameters are met).
  * Able to swallow oral medication.
  * Willing to be randomized to any of the diet arms and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations
  * Women must be of postmenopausal status. Postmenopausal status is defined by any one of the following criteria:
* Prior bilateral oophorectomy or current ovarian suppression with a GnRH agonist
* Age ≥60 years
* Age \<60 years and amenorrheic for at least 12 months (spontaneous cessation of menses for 12 consecutive months or more in the absence of chemotherapy

Exclusion Criteria:

* Multiple prior lines of chemotherapy in the metastatic setting (One line of chemotherapy is allowed. Also prior treatment with CDK4/6 inhibitors is allowed)
* Currently participating in a study of an investigational agent
* Current participation in a formalized weight loss program or currently consuming a ketogenic diet
* Body mass index \< 20 kg/m\^2
* Known hypersensitivity to alpelisib, fulvestrant, canagliflozin, or to any of the excipients of alpelisib or fulvestrant.
* Concurrent malignancy (basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or cervical cancer in situ that have undergone curative intent therapy are allowed)
* Type 1 diabetes mellitus
* Uncontrolled type 2 diabetes mellitus (hemoglobin A1c ≥8.0)
* Type 2 diabetes mellitus requiring treatment with a sulfonylurea, meglitinide, SGLT2 inhibitors or insulin.
* Vegetarian or vegan eating habits.
* Allergy or intolerance to egg, gluten, nut or milk protein that would interfere with adherence to diet.
* Individuals with impaired decision making capacity