Epcoritamab Compared to Observation for Treating B-cell Lymphoma Patients Not in Complete Remission After CD19-directed CAR-T Therapy

Inclusion Criteria:

* Men and women \>= 18 years of age
* Documented histological confirmation of diffuse large b-cell lymphoma not otherwise specified \[DLBCL NOS\], primary mediastinal large b-cell lymphoma (LBCL), or transformations of indolent B-cell lymphomas, according to the 5th edition of World Health Organization (WHO) classification of lymphoid neoplasms, with CD20 positivity as determined by assessment of tumor cells =\< 6 months prior to registration pre- CAR-T biopsy specimen by immunohistochemistry or flow cytometry
* Patients treated with the commercially available CD19-directed CAR-T products axicabtagene ciloleucel (axi-cel), tisagenlecleucel (tisa-cel), or lisocabtagene maraleucel (liso-cel), and who have a partial response at day 30 +/- 7 days PET- CT assessment based on Lugano criteria (Deauville score of 4 or 5)
* Documented measurable disease
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2. (Form is available on the Academic and Community Cancer Research United \[ACCRU\] web site under Study Resources -\> Forms)
* Absolute neutrophil count (ANC) \>= 1,000/mm\^3, granulocyte colony stimulating factor (G-CSF) allowed (obtained =\< 14 days prior to registration)
* Platelet count \>= 50,000/mm\^3 (obtained =\< 14 days prior to registration)
* Hemoglobin \>= 7.0 g/dL if asymptomatic or hemoglobin \> 8 if symptomatic; transfusion support allowed, if necessary (obtained =\< 14 days prior to registration)

  * NOTE: symptoms include shortness of breath, fatigue, lightheadedness
* Total bilirubin =\< 1.5 x upper limit of normal (ULN) unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin or lymphoma involvement of the liver and total bilirubin is =\< 5 x ULN (obtained =\< 14 days prior to registration)
* Alanine aminotransferase (ALT) and aspartate transaminase (AST) =\< 3 x ULN (=\< 5 x ULN for patients with liver involvement) (obtained =\< 14 days prior to registration)
* Calculated creatinine clearance must be \>= 45 mL/min using the Crockcroft- Gault formula (obtained =\< 14 days prior to registration)

  * NOTE: If your site laboratory reports use different units of measurement than what is required by the protocol eligibility requirements, please use the "Lab Test Unit Conversion Worksheet" available on the ACCRU website under "General Forms."
* Negative serum pregnancy test done =\< 7 days prior to registration for a woman of childbearing potential (WOCBP) only

  * NOTE: A WOCBP is a sexually mature female who:

    * Has not undergone a hysterectomy or bilateral oophorectomy; or
    * Has not been naturally postmenopausal for at least 12 consecutive months (i.e., has had menses at any time in the preceding 12 consecutive months)
* Provide informed written consent =\< 28 days prior to registration
* Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study, i.e., active treatment and clinical follow-up)
* Willing to provide mandatory tissue specimens and blood specimens for correlative research purposes

Exclusion Criteria:

* Patients post CAR-T who have bulky disease defined as a disease focus \>= 7.5cm in diameter at day 30 +/- 7 days PET-CT assessment
* Patients post CAR-T who have progressive disease, stable disease or complete response at day 30 +/- 7 days PET-CT assessment based on Lugano criteria
* Any of the following because this study involves an investigational agent whose genotoxic, mutagenic, and teratogenic effect on the developing fetus and newborn are unknown

  * Pregnant persons
  * Nursing persons
  * Persons of childbearing potential who are unwilling to employ adequate contraception (men and women)
* Any of the following prior therapies:

  * CD20xCD3 bispecific antibody at any point prior to registration
  * CD20-targeted monoclonal antibody (e.g., rituximab, obinutuzumab or biosimilars) =\< 4 weeks prior to registration
* Ongoing cytokine release syndrome (CRS) or neurotoxicity post CAR-T
* Prior grade 4 CRS or neurotoxicity after most recently administered CAR-T
* Primary central nervous system (CNS) lymphoma or CNS involvement by lymphoma at screening and based on clinical symptoms, MRI, or lumbar puncture
* Co-morbid systemic illness or other severe concurrent disease which, in the judgement of the investigator, would make the patient inappropriate for entry into the study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens
* Uncontrolled intercurrent illness including, but not limited to:

  * Ongoing or active infection requiring systemic treatment (excluding prophylactic treatment) =\< 14 days prior to registration, including COVID- 19 infection.

    * NOTE: If evidence of chronic hepatitis B virus (HBV) infection, HBV viral load must be undetectable and on suppressive therapy.
    * NOTE: If history of treated hepatitis C virus (HCV) infection, HCV viral load must be undetectable.
    * NOTE: Patients known to be human immunodeficiency virus (HIV) positive, but stable on anti-retroviral therapy with an undetectable HIV viral load pre-CART, are eligible for this trial.
    * NOTE: Simple urinary tract infection (UTI) and uncomplicated bacterial pharyngitis are permitted if responding to active treatment
    * NOTE: Past COVID-19 infection may be a risk factor, but if resolved symptoms and the subject is vaccinated, they may be enrolled
  * Symptomatic congestive heart failure (New York Heart Association \[NYHA\] class 3 or 4)
  * Unstable angina pectoris
  * Unstable cardiac arrhythmia present =\< 14 days prior to registration
  * Psychiatric illness/social situations that would limit compliance with study requirement
  * History or presence of CNS disorder such as seizure disorder (not including resolved childhood febrile seizures), cerebrovascular ischemia/hemorrhage (not including transient ischemic attacks), cerebellar disease, or any autoimmune disease with CNS involvement
* Receiving any other investigational agent which would be considered treatment for the primary neoplasm =\< 14 days prior to registration
* Other active malignancy requiring therapy \< 2 years prior to registration (localized non-melanoma skin cancer is allowed)
* Clinically significant cardiovascular disease, including: Myocardial infarction within 1 year prior to randomization, or unstable or uncontrolled disease/condition related to or affecting cardiac function (eg, unstable angina, congestive heart failure, New York Heart Association class III-IV) cardiac arrhythmia (Common Terminology Criteria for Adverse Events \[CTCAE\] version 5.0 grade 2 or higher), or clinically significant electrocardiogram (ECG) abnormalities