Rituximab and LMP-Specific T-Cells in Treating Pediatric Solid Organ Recipients With EBV-Positive, CD20-Positive Post-Transplant Lymphoproliferative Disorder

Inclusion Criteria:

* Patient must have a history of solid organ transplantation
* Patients must have biopsy-proven newly diagnosed, relapsed or refractory polymorphic or monomorphic PTLD using the World Health Organization (WHO) classification and that is:

* CD20 positive
* EBV positive by Epstein-Barr virus early ribonucleic acid (RNA) (EBER) in situ hybridization (preferred) and/or LMP immunoperoxidase staining
* There must be evaluable disease at study entry either by imaging or by serial endoscopic biopsies.

* Note: a measurable node must have an LDi (longest diameter) greater than 1.5 cm; a measurable extranodal lesion should have an LDi greater than 1.0 cm; all tumor measurements must be recorded in millimeters (or decimal fractions of centimeters)
* Patients must be considered medically refractory to decreased immunosuppression (50% or greater reduction) for at least 1 week or there must be documentation in the medical chart that decreased immunosuppression would be associated with an unacceptable risk of rejection
* Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0 or 1

* Use Karnofsky for patients \> 16 years of age and Lansky for patients =\< 16 years of age
* Patients must have a life expectancy of \>= 8 weeks
* Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering this study
* Myelosuppressive chemotherapy: must not have received within 2 weeks of entry onto this study
* COHORT A and B: Patient must not have received therapy with anti-CD20 monoclonal antibodies within 90 days of entry onto this study
* COHORT C: Patient must have received rituximab at 375 mg/m\^2 weekly for at least 3 doses within the last 90 days prior to study enrollment
* Must not have received any prior radiation to any sites of measurable disease
* Must not have received any prior stem cell transplant
* Must not have received investigational therapy within 30 days of entry onto this study
* Must not have received prior EBV or LMP-specific T cells within 90 days of entry onto this study
* Must not have received alemtuzumab or other anti-T-cell antibody therapy within 28 days of entry onto this study
* COHORT C: HLA typing is available and will be submitted at the time of enrollment.

Exclusion Criteria:

* Burkitt morphology
* Central nervous system (CNS) involvement; CNS status must be confirmed by lumbar puncture

* Note: lumbar puncture can be performed at the time of diagnosis and does not need to be repeated unless there is a change in neurological status or it was performed more than 14 days prior to study entry
* Bone marrow involvement (\> 25%)

* Note: bone marrow aspiration/biopsy can be performed at the time of diagnosis and does not need to be repeated unless there is a change in peripheral blood counts or it was performed more than 14 days prior to study entry
* Fulminant PTLD defined as: fever \> 38 degrees Celsius (C), hypotension, and evidence of multi-organ involvement/failure including two or more of the following:

* Bone marrow (including pancytopenia without any detectable B-cell proliferation)
* Liver (coagulopathy, transaminitis and/or hyperbilirubinemia)
* Lungs (interstitial pneumonitis with or without pleural effusions)
* Gastrointestinal hemorrhage
* Any documented donor-derived PTLD
* Hepatitis B or C serologies consistent with past or current infections because of the risk of reactivation with rituximab
* Severe and/or symptomatic refractory concurrent infection other than EBV
* Pregnant females are ineligible since there is no available information regarding human fetal or teratogenic toxicities
* Lactating females are not eligible unless they have agreed not to breastfeed their infants
* Female patients of childbearing potential are not eligible unless a negative pregnancy test result has been obtained
* Sexually active patients of reproductive potential are not eligible unless they have agreed to use an effective contraceptive method for the duration of their study participation and for 12 months following completion of study therapy.
* All patients and/or their parents or legal guardians must sign a written informed consent
* All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met