Safety/Efficacy of MEDI-551 in Combination With Immunomodulating Therapies in Subjects With Aggressive B-cell Lymphomas

Key inclusion criteria: * Histologically confirmed aggressive diffuse large B-cell lymphoma (DLBCL), including follicular lymphoma (FL) transforming to DLBCL, transformed indolent lymphoma, mantle cell lymphoma (MCL), or Grade 3B FL for dose-escalation cohorts. Only participants with DLBCL will be enrolled in the dose-expansion cohort. * Willing to provide a fresh tumor sample * Evaluable/measurable disease with measurable disease defined as greater than or equal to (\>= 1) lesion less than or equal to (\<=) 20 mm in one dimension or ≥ 15 mm in 2 dimensions as measured by conventional or high-resolution (spiral) computed tomography (CT). Disease evaluable by the International Working Group criteria (Cheson et al, 2007). (NOTE: Irradiated lesions will not be evaluable.) * Baseline fludeoxyglucose positron emission tomography (FDG-PET) or FDG-PET/CT scans must show positive lesions compatible with CT-defined anatomical tumor sites. * Relapsed from or refractory to \>= 2 prior chemotherapy regimens with \>= 1 regimen containing rituximab or failed 1 prior rituximab-containing regimen and unable to tolerate additional multiagent chemotherapy. NOTE: Subjects enrolled in the dose-escalation portion of the study must have exhausted all available standard therapy. * At least 100 days past autologous stem cell transplant (ASCT). * At least 1 year past allogeneic stem-cell transplant (SCT) and off immunosuppression therapy, with no evidence of graft-versus-host disease. * Eastern Cooperative Oncology Group performance status 0-2. * Adequate hematological function * Adequate organ function * Females of childbearing potential who are sexually active with a nonsterilized male partner must use a highly effective method of contraception for 30 days prior to the first dose of investigational product, and must agree to continue using such precautions for 180 days after the final dose of investigational product. * Nonsterilized males who are sexually active with a female partner of childbearing potential must use a highly effective method of contraception from Day 1through 90 days after receipt of the final dose of investigational product. Key exclusion criteria: * Any concurrent chemotherapy, radiotherapy, immunotherapy, biologic or hormonal therapy for treatment of cancer. * Receipt of any experimental therapy, mAb, cancer vaccine, chemotherapy or small molecule within 28 days prior to Cycle 1 Day 1 or 5 half-lives of that therapy, whichever is shorter. * Previous therapy directed against cluster of differentiation 19 (CD19) * Prior exposure to immunotherapy such as but not limited to other anti-cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4), anti-PD 1, or anti-PD-L1 antibodies excluding cancer vaccines. * Vaccination with a live virus within 28 days prior to receiving the first dose of study drug * History of other invasive malignancy within 2 years except for cervical carcinoma in situ, non-melanomatous carcinoma of the skin or ductal carcinoma in situ of the breast that has been surgically cured. * Evidence of significant active infection requiring antimicrobial, antifungal, antiparasitic, or antiviral therapy or for which other supportive care is given unless the subject is clinically stable. * Human immunodeficiency virus (HIV) positive serology or acquired immunodeficiency syndrome (AIDS). * Active hepatitis B * Ongoing \>= Grade 2 toxicities from previous cancer therapies or any unresolved \> Grade 1 immune-related adverse event (irAE) event unless specifically allowed in the inclusion/exclusion criteria. * No immunosuppressive therapy within 14 days of Cycle 1 Day 1 of MEDI0680 (AMP-514) dosing. * Active or prior documented autoimmune or inflammatory disease except vitiligo. * History of primary immunodeficiency. * Major surgical procedures (as defined by the principal investigator) within 28 days of Cycle 1 Day 1 or still recovering from prior surgery. * History of tuberculosis, including those who may have completed prophylactic isoniazid (INH) therapy. * Documented current central nervous system (CNS) involvement, leptomeningeal disease, or spinal cord compression. * Pregnancy or lactation. * Clinically significant abnormality on electrocardiogram (ECG). * Uncontrolled inter-current illness including, but not limited to, ongoing or active infection, current pneumonitis, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs from MEDI-551 or MEDI0680 (AMP-514), or compromise the ability of the subject to give written informed consent.