4-1BB Agonist Monoclonal Antibody PF-05082566 With Trastuzumab Emtansine or Trastuzumab in Treating Patients With Advanced HER2-Positive Breast Cancer

INCLUSION CRITERIA: * History of biopsy proven HER2 overexpressing breast cancer and radiographic evidence of metastatic disease, or locally recurrent unresectable disease. The HER2 status can be determined either by immunohistochemistry (IHC) \[IHC score, 3+\] or by fluorescence in situ hybridization (FISH) \[as defined by HER2/CEP 17 ratio ≥ 2.0, or HER2 copy number ≥ 6\], or as otherwise defined by 2018 ASCO/CAP guidelines. * Cohort 1 subjects must have received trastuzumab and a taxane separately or in combination (those who previously received ado-trastuzumab emtansine may accrue to Cohort 2). * Subjects in Cohort 2 must have received at least 1 prior therapy including ado-trastuzumab emtansine. * Subjects who discontinued prior trastuzumab or ado trastuzumab emtansine due to progressive or refractory disease are eligible for enrollment * Available tumor samples. For eligibility, if no unstained slides remain, stained pathology slides may be reviewed at the treating institution. However, a tumor sample is required for research evaluations per the following (any of Item 1; 2; or 3, in order of preference). * A FFPE tumor tissue block from a de novo fresh tumor biopsy obtained during screening will be requested, though not mandated. * A recently obtained archival FFPE tumor tissue block (or 10 to 15 unstained slides) from a primary or metastatic tumor resection or biopsy if the following criteria are met: * The biopsy or resection was performed within 1 year of enrollment OR * The subject has not received any intervening systemic anti cancer treatment from the time the tissue was obtained and enrolled onto the current study. OR * Any archival FFPE tumor tissue block (or unstained slides) from primary tumor resection specimen (if not provided per above). The archival sample may have been collected at any time prior to the current study, regardless of any intervening therapy. If an FFPE tissue block cannot be provided, a minimum of 10 unstained slides (15 preferable) will be acceptable. * Subjects must have evaluable OR measurable disease, as defined by RECIST v1.1. * Performance status 0 to 1 (by Eastern Cooperative Oncology Group \[ECOG\] scale). * Laboratory parameters (must satisfy all): Absolute neutrophil count (ANC) ≥ 1.5 × 109/L (≥ 1500/µL) Platelet count ≥ 100 × 109/L (≥ 100,000 /µL) Hemoglobin ≥ 9.0 g/dL; subjects on therapeutic anticoagulation are eligible if there is no bleeding and they are on a stable dose of anticoagulation therapy (eg, on Coumadin with an INR of 2 to 3) for at least 7 days before registration (prior to the start of therapy, or stable heparin or Factor Xa inhibitor dose) Serum creatinine ≤ 1.5 × the ULN or calculated creatinine clearance (by Cockcroft Gault formula) ≥ 60 mL/min Aspartate aminotransferase (AST) ≤ 2.5 × ULN Alanine aminotransferase (ALT) ≤ 2.5 × ULN Bilirubin ≤ 1.5 × ULN * Subjects must not be pregnant or breastfeeding. A pregnancy test will be obtained if the subject is a woman of child bearing potential, defined as a sexually mature woman who has not undergone a hysterectomy or and/or bilateral oophorectomy or who has not been naturally postmenopausal for at least 24 consecutive months (ie, who has had menses at any time in the preceding 24 consecutive months) with 2 pregnancy tests, one at screening, and another immediately preceding the initiation of treatment. * Subjects must have signed an informed consent document stating that they understand the investigational nature of the proposed treatment * Left ventricular ejection fraction determined by echocardiogram or multiple gated acquisition scan (MUGA) (cardiac scan) must be 50% or higher. EXCLUSION CRITERIA: * Previously discontinued either trastuzumab or ado trastuzumab emtansine due to intolerance. * Received any other investigational agents within 30 days of registration. * Central nervous system (CNS) metastases, unless previously treated by either radiation therapy and/or surgical resection, clinically stable for at least 60 days and on a stable corticosteroid dose of ≤ 4 mg/day decadron (or equivalent steroid regimen) for at least 1 month. Subjects with a history of CNS metastases that are both treated and stably controlled are eligible if all of the following apply: * Therapy has been administered (surgery and/or radiation therapy); * There is no additional treatment planned for brain metastases; * The subject is clinically stable; * The subject is on a stable corticosteroid dose of ≤ 4 mg/day decadron (or equivalent steroid regimen) for at least 1 month. * Prior malignancy (other than in situ cervical cancer, or basal cell or squamous cell carcinoma of the skin), unless treated with curative intent and without evidence of disease for 3 years or longer * Administration of other prior anticancer therapies within 4 weeks of enrollment, except ongoing administration of a bisphosphonate drug or denosumab as treatment for bone metastasis * Toxicities related to prior anticancer treatment (except alopecia) that have not resolved to ≤ Grade 1 according to common terminology criteria for adverse events (CTCAE v5) before registration or prior to start of therapy * Currently receiving systemic antibiotic, antiviral, or antifungal therapy for the treatment of an active infection * Systemic corticosteroid therapy at doses of greater than prednisone 5 mg daily (or dose-equivalent chronic steroid regimen) for therapeutic and not adrenal replacement indications (maintenance steroid use for adrenal insufficiency is permitted). Acute emergency administration, topical applications, inhaled sprays, eye drops or local injections of corticosteroids are allowed. * History of bleeding diathesis * Any co morbid medical condition deemed by the treating or principal investigator to possibly put the subject at significant risk for toxicity. * Subject has known sensitivity to any of the products to be administered during dosing * Subject has any kind of disorder that compromises the ability of the subject to give written informed consent and/or to comply with study procedures * Uncontrolled intercurrent illness including, but not limited to, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * History of venous thromboembolism within prior 6 months. * Subject with reproductive potential who will not agree to use, during the study and for 60 days after the last dose of utomilumab or 6 months for ado trastuzumab emtansine or trastuzumab 2 highly effective method of contraceptive such as: * Implants * Injectables * Intrauterine devices (IUDs) such as copper T or Levonorgestrel releasing intrauterine system (LNG IUS) * Sexual abstinence * Vasectomized partner * Condom or occlusive cap (diaphragm or cervical/vault cap) supplemented with the use of a spermicide during treatment