Part A - Pathologically confirmed estrogen and/or progesterone receptor (ER/PR) positive and HER2 negative locoregionally recurrent or metastatic breast cancer - At least one target or non-target lesion per RECIST v1.1 criteria. - Male or non-pregnant, non-lactating female subjects age ≥18 years. Part B - Pathologically confirmed estrogen and/or progesterone receptor (ER/PR) positive and HER2 negative locoregionally recurrent or metastatic breast cancer - Refractory to endocrine therapy. Note: there is no limit on prior number of lines of endocrine therapy or prior treatments with CDK4/6, AKT, PI3K and/or mTOR inhibitors. - Received or declined at least one line of chemotherapy or antibody drug conjugate in the locoregionally recurrent or metastatic setting - Progressive disease or intolerance to last treatment. - At least one target lesion per RECIST v1.1 criteria. - Male or non-pregnant, non-lactating female subjects age ≥18 years. - Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1. - Life expectancy of at least six months. - Adequate bone marrow reserve, hepatic function and renal function.

Part A - Study participant has not recovered from clinically significant adverse event(s) resulting from most recent anticancer therapy/intervention. - Known central nervous system (CNS) disease, except for those subjects with treated brain metastasis who are stable for at least 1 month, having no evidence of progression or hemorrhage after treatment and no ongoing requirement for corticosteroids, as ascertained by clinical examination and brain imaging (magnetic resonance imaging [MRI] or computed tomography [CT]) during the screening period. - Radiotherapy for breast cancer ≤ 28 days prior - Received a radionuclide within a period of less than 10 physical half-lives of the administered radionuclide prior to dosing with 68Ga-R11228. - Any condition that precludes the proper performance of imaging procedures required in this study. Part B - Study participant has not recovered from clinically significant adverse event(s) resulting from most recent anticancer therapy/intervention - Treatment with anticancer therapy or with an investigational drug or device within 21 days or 5 half-lives of the agent (whichever is shorter) - Known central nervous system (CNS) disease, except for those subjects with treated brain metastasis who are stable for at least 1 month, having no evidence of progression or hemorrhage after treatment and no ongoing requirement for corticosteroids, as ascertained by clinical examination and brain imaging (magnetic resonance imaging [MRI] or computed tomography [CT]) during the screening period. - Radiotherapy for breast cancer ≤ 28 days - Prior systemic radionuclide therapeutic treatment. - Received a radionuclide within a period of less than 10 physical half-lives of the administered radionuclide prior to dosing with 68Ga-R11228. - Any unresolved NCI-CTCAE Version 5.0 Grade 2 or higher toxicity (except alopecia and Grade 2 platinum-therapy related neuropathy) from previous breast cancer treatment and/or from medical/surgical procedures or interventions. - Any condition that precludes the proper performance of imaging procedures required in this study.