Study to Evaluate the Safety and Antitumor Activity of CX-2009 Monotherapy and in Combination With CX-072 in Advanced Breast Cancer

INCLUSION CRITERIA: * Arm A: inoperable, locally advanced or metastatic HR-positive/HER2-negative breast cancer. Patients must have received 0 to 2 prior cytotoxic chemotherapy in the inoperable, locally advanced, or metastatic setting * Arm B and Arm C: inoperable, locally advanced or metastatic TNBC; archival or fresh tumor tissue must have high CD166 expression by immunohistochemistry (IHC). Patients must have received 1 - 3 prior lines of therapy for inoperable, locally advanced, or metastatic TNBC * Arm C only: Patients must be Programmed Death Ligand 1 (PD-L1) positive by an FDA-approved test. For patients who have received prior checkpoint inhibitors (CPI) therapy: if the CPI was the most recent treatment given prior to enrollment into this study, the patient must not have progressed within 120 days of the first dose of the CPI * Measurable disease per RECIST v1.1 * Adults, at least 18 years of age * Eastern Cooperative Oncology Group performance status of 0 or 1 * Adequate baseline Laboratory Values * Patients of childbearing potential or those with partners of childbearing potential must agree to use a highly effective method of birth control at least 1 month prior to first dose, during study treatment, and for a period of 50 days after the last dose of CX-2009 and 105 days after the last dose of CX-072 (Arm C). * Patients with brain metastases that are ≤ 1 cm, are asymptomatic, and require no treatment may be eligible after discussion with Medical Monitor. * Additional inclusion criteria may apply EXCLUSION CRITERIA: * History of malignancy that was active within the previous 2 years. Exceptions include localized cancers that are not related to the current cancer being treated, that are considered to have been cured, and in the opinion of the Investigator present a low risk for recurrence * Untreated symptomatic brain and/or leptomeningeal metastases * Unresolved prior therapy-related acute toxicity Grade \> 1, including neuropathy. Alopecia and other nonacute toxicities are not exclusionary * Active or chronic corneal disorder * Serious concurrent illness * History of allogeneic tissue/solid organ transplant, stem cell transplant, or bone marrow transplant * Arm C only: * History of or current active autoimmune diseases * History of myocarditis regardless of the cause * History of intolerance to prior immune CPI therapy defined as the need to discontinue treatment due to an immune-related Adverse Event (AE) * Immunosuppressive therapy including chronic systemic steroid (≥ 10 mg daily prednisone equivalents) within 14 days of Cycle 1 Day 1 (C1D1). However, patients who require brief courses of steroids (eg, as prophylaxis for IV contrast or for treatment of an allergic reaction) may be eligible with Medical Monitor approval. Inhaled or topical steroids are permitted. * History of severe allergic or anaphylactic reactions to previous monoclonal antibody (mAb) therapy or known hypersensitivity to any component of Probody therapeutic * Prior treatment with maytansinoid-containing drug conjugates (eg, DM1 or DM4 antibody drug conjugate, including trastuzumab emtansine) * Pregnant or breastfeeding * Additional exclusion criteria may apply