A Study to Learn About a New Medicine Called Vepdegestrant (ARV-471, PF-07850327) in People Who Have Advanced Metastatic Breast Cancer

A study to learn about a new medicine called ARV-471 (PF-07850327) in people who have advanced metastatic breast cancer.

The purpose of this study is to learn about the safety and effects of the study medicine ARV-471 (PF-07850327, vepdegestrant) compared to fulvestrant (FUL) in participants with advanced breast cancer. Advanced breast cancer is difficult to cure or control with treatment. The cancer may have spread from where it first started to nearby tissue, lymph nodes, or distant parts of the body, i.e. bones, lungs, brain, or liver. FUL is a medicine already used for treatment of breast cancer while ARV-471 is a new medicine. This study is seeking participants with breast cancer who: * have cancer that has come back in the place where it started or spread to nearby tissue, lymph nodes, or distant parts of the body. * cannot be fully cured by surgery or radiation therapy. Radiation therapy is the use of high-energy radiation such as x-rays, gamma rays and other sources to kill cancer cells and shrink tumors. * respond to hormonal or endocrine therapy (which target hormones and/or activity of hormone receptors) such as tamoxifen or aromatase inhibitors (this is called estrogen receptor positive disease) * have received one line of CDK4/6 inhibitor therapy (for example palbociclib, ribociclib or abemaciclib) in combination with endocrine therapy (for example letrozole) for advanced cancer. * are allowed up to one other endocrine therapy (for example exemestane) for advanced cancer. Half of the participants will be given ARV-471 while the other half of the participants will be given FUL. Participants who get ARV-471 will take ARV-471 by mouth with food, one time a day. During the first treatment cycle participants who will get FUL will be given FUL by shots into the muscles on Day 1 and again 2 weeks later. After the first month, FUL shots will be given on the first day of each new treatment cycle. One treatment cycle is 28 days. Participants will receive the study medicine until their breast cancer worsens or side effects become too severe. Participants will have visits at the study clinic about every 4 weeks.

Inclusion Criteria: * Adult participants with loco-regional recurrent or metastatic breast disease not amenable to surgical resection or radiation therapy * Confirmed diagnosis of ER+/HER2- breast cancer * Prior therapies for locoregional recurrent or metastatic disease must fulfill all the following criteria: * One line of CDK4/6 inhibitor therapy in combination with endocrine therapy. Only one line of CDK4/6 inhibitor is allowed in any setting. * ≤ 1 endocrine therapy in addition to CDK4/6 inhibitor with ET * Most recent endocrine treatment duration must have been given for ≥6 months prior to disease progression. This may be the endocrine treatment component of the CDK4/6 inhibitor line of therapy. * Radiological progression during or after the last line of therapy. * Measurable disease evaluable per Response Evaluation Criterion in Solid Tumors (RECIST) v.1.1 or non-measurable bone-only disease * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 * Participants should be willing to provide blood and tumor tissue Exclusion Criteria: * Participants with advanced, symptomatic visceral spread, that are at risk of life-threatening complications in the short term * Prior treatment with: * ARV-471, fulvestrant, elacestrant, mTOR, PI3K, AKT pathway inhibitors, PARP inhibitor for any setting * other investigational agents (including novel endocrine therapy any SERDs, SERCAs, CERANs) for any setting * prior chemotherapy for advanced/metastatic disease * Inadequate liver, kidney and bone marrow function * Active brain metastases * Participants with significant concomitant illness