Adding Capivasertib to Standard Treatment in HR Positive, HER2 Negative Metastatic Breast Cancer Based on ctDNA Testing

Registration Step 1 Inclusion Criteria: * Participants must have histologically or cytologically confirmed adenocarcinoma of the breast with unresectable or metastatic disease. * Participants must have evidence of either 1) measurable disease with or without non-measurable disease, or 2) non-measurable disease only, but the non-measurable disease must include bone metastases. Participants must have a CT scan or MRI of the chest and abdomen AND a whole-body bone scan within 28 days prior to registration. X-rays, scans, or other tests for assessment of non-measurable disease must have been performed within 42 days prior to registration. All disease must be assessed and documented on the Baseline Tumor Assessment Form. Note: Participants cannot have only non-measurable disease without bone involvement. * Participants must have HER2-negative breast cancer, defined as a negative in situ hybridization test or an IHC status of 0 or 1+. If IHC is 2+ (i.e. indeterminate), a negative in situ hybridization (FISH, CISH, or SISH) test is required by local laboratory testing (as per the ASCO-CAP guidelines). * Participants' most recent tumor biopsy or surgical resection specimen must be either ER-positive, PgR-positive, or both, as defined by immunohistochemistry (IHC) ≥1% (as per the ASCO-CAP guidelines). * Female participants must be at post-menopausal status or be receiving ovarian ablation with a GnRH agonist such as goserelin. Pre-menopausal (and peri-menopausal, i.e. those that do not meet the criteria defined for post-menopausal below) women are eligible if amenable to treatment with an GnRH agonist. Male participants should also receive GnRH agonist. These participants must begin concomitant treatment with GnRH agonist at least 14 days prior to Cycle 1, Day 1 and must be willing to continue concomitant treatment for the duration of the study. Post-menopausal status is defined by any one of the following criteria: Prior bilateral oophorectomy, Age ≥60 years, or Age \<60 and amenorrhea for 12 months following cessation of all exogenous hormonal treatments/chemotherapy/ovarian suppression/tamoxifen or similar. Participants should also have serum estradiol and follicle stimulating hormone (FSH) levels confirmed as being within the standard laboratory reference range for post-menopausal females per local institution standards. * Participants must be ≥ 18 years old at the time of registration. * Participants must have Zubrod Performance Status of 0 or 1. * Participants must have a complete medical history and physical exam within 28 days prior to registration. * Participants must have adequate organ and marrow function within 28 days prior to registration. * Participants must have a calculated creatinine clearance ≥ 50 mL/min using the Cockcroft-Gault Formula. This specimen must have been drawn and processed within 28 days prior to registration. For creatinine clearance formula see the tools on the CRA Workbench https://txwb.crab.org/TXWB/Tools.aspx. * Participants must be given the opportunity to participate in the Patient-Reported Outcomes version of the Common Terminology Criteria for Adverse Events (PRO-CTCAE) form. * Participants must agree to have blood specimens submitted for ctDNA molecular response assessment. * Participants must be offered the opportunity to participate in planned non-real time ctDNA analysis. Registration Step 1 Exclusion Criteria: * Participants must not have active central nervous system (CNS) disease or evidence of active leptomeningeal disease. * Participants must not have had endocrine resistance as defined as breast cancer recurrence within 12 months of cessation of endocrine therapy in the adjuvant setting. Prior adjuvant CDK4/6 inhibitor use is allowed as long as participants did not have a recurrence within 12 months of completion of treatment with an adjuvant CDK4/6 inhibitor. * Participants must not have initiated, but must be planning to initiate, NSAI + palbociclib or ribociclib as the initial therapy for unresectable or metastatic disease. * Participants must not have received prior systemic therapy in the metastatic setting, including chemotherapy or hormone therapy. Prior exposure to any chemotherapy or anti-cancer agents including hormonal therapy in the (neo)adjuvant setting is allowed as long as appropriate washout period before randomization/enrollment is met. * Participants must not be concurrently using hormone replacement therapy. * Participants must not have received prior fulvestrant or PI3K/AKT inhibitor treatment. * Participants must not have received strong inhibitors or potent inducers or substrates of CYP3A4 or substrates of CYP2D6 within 14 days (21 days for St. John's Wort) prior to registration. * Participants must agree to not use herbal or natural products intended as treatment or prophylaxis for any type of cancer. * Participants must not have radiotherapy within 14 days prior to the Step 1 registration. * Participants must not have a major surgical procedure (excluding placement of vascular access) or significant traumatic injury within 28 days prior to Step 1 registration or an anticipated need for major surgery during the study. * Participants must not have any unresolved toxicities from prior therapy greater than Common Terminology Criteria for Adverse Events (CTCAE) grade 1 at the time of registration with the exception of alopecia, lymphocyte decrease, grade 2 lymphopenia and grade 2 prior chemotherapy-therapy related neuropathy. * Participants must not have uncontrolled diabetes mellitus or risk for hyperglycemia within 28 days prior to registration. Participants must plan to have serum glucose performed prior to beginning Step 1 treatment. * Participants with known human immunodeficiency virus (HIV) infection must be on effective anti-retroviral therapy at registration and have undetectable viral load on the most recent test results prior to registration. All of the following criteria are required to define an HIV infection that is well controlled: undetectable viral RNA load, CD4+ count of \> 350, no history of AIDS-defining opportunistic infection within the past 12 months, and on anti HIV medications for at least 28 days. Note: Lower CD4+ count values are acceptable if clinically indicated and the participant has a potentially curable malignancy or for interventions in a later stage of development that have demonstrated prior activity within a given cancer. * Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. Participants currently being treated for HCV infection must have undetectable HCV viral load test on the most recent test results, if indicated. * Participants must not have acute hepatitis B. Participants with a known history of chronic hepatitis B virus (HBV) infection must have both a negative HBsAg result and an HBV DNA viral load below the lower limit of quantification on the most recent test results prior to registration. Participants with a positive HBsAg due to recent vaccination are eligible if HBV DNA viral load is below the lower limit of quantification. Note: Participants receiving anti-viral therapies which are strong inhibitors or inducers of CYP3A4 will be excluded due to the potential for drug-drug interaction with capivasertib. * Participants must not have impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs (e.g. ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection). * Participants with a history of CNS metastases or cord compression must have been clinically stable (i.e. non-active disease) for at least 28 days since completion of definitive treatment and must not be receiving systemic steroids. In the case of brain metastases, the participant must have stable or improved imaging at least 4 weeks after completion of definitive treatment. * Participants must not have or had a prior or concurrent malignancy whose natural history or treatment (in the opinion of the treating physician) has the potential to interfere with the safety or efficacy assessment of the study regimen. * Participants must not have clinically significant, uncontrolled heart disease and/or cardiac repolarization abnormality, as confirmed by triplicate ECG within 28 days prior to registration. * Participants must not have a major known bleeding disorder (e.g., bleeding diathesis) or be receiving anticoagulant therapy that would preclude intramuscular administration of fulvestrant or Luteinizing Hormone-Releasing Hormone (LHRH) agonists. * Participants must not have a history of (noninfectious) interstitial lung disease (ILD)/pneumonitis that required steroids or have current ILD/pneumonitis symptoms. * Participants must not be pregnant or nursing (nursing includes breast milk fed to an infant by any means, including from the breast, milk expressed by hand, or pumped). Individuals who are of reproductive potential must have agreed to use an effective contraceptive method with details provided as a part of the consent process. A person who has had menses at any time in the preceding 12 consecutive months or who has semen likely to contain sperm is considered to be of "reproductive potential." In addition to routine contraceptive methods, "effective contraception" also includes refraining from sexual activity that might result in pregnancy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) including hysterectomy, bilateral oophorectomy, bilateral tubal ligation/occlusion, and vasectomy with testing showing no sperm in the semen. Participants must have a negative urine pregnancy test within 14 days prior to registration.