PACIFIC: Primary Mediastinal Large B-cell Lymphoma Treated With Antibody Therapy, Checkpoint Inhibitor in Frontline With ImmunoChemotherapy

Inclusion Criteria:

* Histopathologically confirmed diagnosis of PMBL

  * Require a CD30 expression level of 1% or greater in the tumor or tumor-infiltrating lymphocytes by local immunohistochemistry
* No prior treatment except

  * A prior limited-field radiotherapy
  * A short course (up to 7 days) of glucocorticoids =\< 100 mg daily of prednisone equivalent which must cease prior to day 1 of cycle 1
* Stage of patients: Stages II, III, IV, and stage I \>= 5 cm in the greatest dimension
* Patient or durable power of attorney (DPA) for healthcare must be able to understand and voluntarily sign an Institutional Review Board (IRB)-approved informed consent form
* Age \>= 18 years at the time of signing the informed consent
* Patients must have bi-dimensional measurable disease, as defined as radiographically apparent disease with the longest dimension of \>= 1.5 cm
* Patients with performance status of =\< 3 (3 only allowed if decline in status is deemed related to lymphoma and felt potentially reversible by the treating physician)
* Serum bilirubin \< 1.5 x ULN except in patients with Gilbert's syndrome as defined by \> 80% unconjugated bilirubin
* Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x ULN or \< 5 x ULN if hepatic metastases are present
* Absolute neutrophil count (ANC) \> 1000/mm\^3 unless deemed related to lymphoma involvement in the bone marrow and felt potentially reversible by the treating physician
* Platelets \> 1000/mm\^3 unless deemed related to lymphoma involvement in the bone marrow and felt potentially reversible by the treating physician
* Calculated creatinine clearance \>= 30 ml/min by Cockcroft-Gault formula
* Patients must be willing to receive transfusions of blood products
* Women of childbearing potential must have a negative serum (beta-human chorionic gonadotropin \[beta-hCG\]) at screening
* Women of childbearing potential and men who are sexually active with a woman of childbearing potential must be practicing a highly effective method of birth control during and after the study (12 months for women and 3 months for men), consistent with local regulations regarding the use of birth control methods for subjects participating in this clinical study. Men must agree to not donate sperm during and for up to 3 months after their conclusion of therapy on study. For females, these restrictions apply for 1 month after the last dose of study drug

Exclusion Criteria:

* Patients with an urgent need for cytoreductive treatment will be excluded
* Any serious medical condition including but not limited to uncontrolled hypertension, uncontrolled congestive heart failure within past 6 months prior to screening (class 3 \[moderate\] or class 4 \[severe\] cardiac disease as defined by the New York Heart Association Functional Classification), uncontrolled diabetes mellitus, active/symptomatic coronary artery disease, chronic obstructive pulmonary disease (COPD), left ventricular ejection fraction (LVEF) less than 40%, renal failure, active infection, history of invasive fungal infection, moderate to severe hepatic disease (Child Pugh class B or C), active hemorrhage, laboratory abnormality, or psychiatric illness that, in the investigators opinion places the patient at unacceptable risk and would prevent the subject from signing the informed consent form. Patients with history of cardiac arrhythmias should have cardiac evaluation and clearance
* Previous anthracycline exposure with expected lifetime exposure to doxorubicin \> 450 mg/m\^2, considering the planned anthracycline exposure in this study with potential six cycles of R-CHP
* Pregnant or lactating females
* Known hypersensitivity to brentuximab vedotin, nivolumab, rituximab, doxorubicin, cyclophosphamide, or prednisone
* Known human immunodeficiency virus (HIV) infection with active viremia

  * Patient with known HIV infection can be included if undetectable viral load, CD4 \>= 300 cells/microL and on HAART (highly active antiretroviral therapy)
* Patients with active viremia of hepatitis B infection

  * Not including patients with prior hepatitis B vaccination; or positive serum hepatitis B antibody
* Patients with active viremia of hepatitis C infection

  * Known hepatitis C infection is allowed as long as there is no active disease and is cleared by gastrointestinal (GI) consultation
* All patients with central nervous system involvement with lymphoma
* Diagnosis of prior malignancy within the past 2 years with the exception of successfully treated basal cell carcinoma, squamous cell carcinoma of the skin, carcinoma "in situ" of the cervix or breast. History of other malignancies are allowed if in remission (including prostate cancer patients in remission from radiation therapy, surgery or brachytherapy), not actively being treated, with a life expectancy \> 3 years
* Significant neuropathy (grades 2 or grade 1 with pain) within 14 days prior to enrollment
* Contraindication to any of the required concomitant drugs or supportive treatments or intolerance to hydration due to preexisting pulmonary or cardiac impairment including pleural effusion requiring thoracentesis or ascites requiring paracentesis not due to lymphoma
* Major surgery within 4 weeks of study entry or wound that is not healed from prior surgery or trauma
* History of stroke or intracranial hemorrhage within 6 months prior to study entry
* Vaccinated with live, attenuated vaccines within 4 weeks of study entry