A Study of Tersolisib (LY4064809/STX-478) With Other Anti-Cancer Treatments in Participants With Advanced Breast Cancer With a Genetic Change (PIK3CA)

Inclusion Criteria:

* Are willing to follow contraception requirements. Contraceptive use by participants should be consistent with local regulations regarding the methods of contraception for those participating in clinical trials.
* If assigned female at birth, pre-/peri- and postmenopausal status is allowed. Those with pre- or peri-menopausal status at study entry must agree to use ovarian function suppression with any locally approved gonadotropin-releasing hormone (GnRH) agonist.
* If assigned male at birth with an estrogen receptor positive (ER+) breast cancer diagnosis, they must agree to use hormone suppression with a GnRH agonist.
* Have histologically or cytologically confirmed breast cancer, defined as individuals with

  * locally advanced breast cancer not amenable to curative therapy (for example, surgery) or metastatic disease, and
  * hormone receptors (HR)+/human epidermal growth factor receptor 2 (HER2)- or HR+/HER low defined by American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) Guidelines

    * HR status: Documented ER+ and/or progesterone receptor-positive (PR+) tumor according to ASCO/CAP Guidelines, defined as greater than or equal to (≥)1 percent (%) of tumor cells stained positive based on the most recent tumor biopsy and assessed locally
    * HER status: immunohistochemistry score of 1+ or score of 2+ with a negative Fluorescence In Situ Hybridization (FISH) based on local results as defined in the ASCO/CAP Guidelines
* Have evidence of an activating PIK3CA mutation, detected in tumor or blood samples using an appropriate assay.
* Have measurable disease or non-measurable, evaluable bone disease
* Part 1:

  * Received 0-2 prior systemic treatments for advanced breast cancer not amenable to curative therapy (for example, surgery) or metastatic disease.
  * Up to 1 of these prior systemic treatments may contain chemotherapy
* Part 2:

  * Received 0 prior systemic treatment for advanced breast cancer not amenable to curative therapy (for example, surgery) or metastatic disease.
  * Individuals who are eligible are either

    * Population 1 (P1): Endocrine sensitive

      * newly diagnosed with advanced breast cancer (de novo)
      * participants with a history of HR+, HER2- EBC and did not receive SOC adjuvant ET
      * relapsed with documented evidence of progression greater than (\>)12 months from completion of (neo)adjuvant ET ± cyclin-dependent kinases 4 and 6 (CDK4/6) inhibitor, or
    * Population 2 (P2): Endocrine resistant

      * relapsed with documented evidence of progression less than or equal to (≤)12 months of completing (neo)adjuvant ET ± CDK4/6 inhibitor.
      * if a CDK4/6 inhibitor was included as part of neoadjuvant or adjuvant therapy, progression event must be \>12 months since completion of CDK4/6 inhibitor portion of neoadjuvant or adjuvant therapy.

Exclusion Criteria:

* Have an established diagnosis of Type 1 diabetes mellitus or Type 2 diabetes mellitus with hemoglobin A1c (HbA1c) ≥8%, fasting blood glucose (FBG) ≥140 milligrams per deciliter (mg/dL) (7.7 millimoles per liter \[mmol/L\]), or requiring insulin.
* Have inflammatory or metaplastic breast cancer.
* History of leptomeningeal disease or carcinomatous meningitis.
* Have known and untreated or active central nervous system (CNS) metastases. Exception: Asymptomatic brain or spinal metastases if treated by surgery, surgery plus radiotherapy, or radiotherapy alone with no evidence of radiographic progression or hemorrhage within at least 28 days before randomization and no requirement for anticonvulsants or systemic corticosteroids for at least 28 days before randomization.
* Have received treatment with any local or systemic antineoplastic therapy or investigational anticancer agent within 14 days or 4 half-lives, whichever is longer, prior to randomization up to a maximum washout period of 28 days.
* Have a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (dose more than 10 milligrams \[mg\] daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to randomization.
* Are pregnant, breastfeeding, or intend to become pregnant during the study or within 6 months of the last dose of study intervention and at least 2 years after the last dose of fulvestrant and/or CDK4/6 inhibitor after the final administration of study treatment.
* Have active bacterial or fungal infection that is not recovered at randomization.