RATIONALE: Reducing the amount of drugs used to prevent transplant rejection may help a person's body kill tumor cells. Giving biological therapy, such as interferon alfa, which may interfere with the growth of cancer cells, or combination chemotherapy, which uses different ways to stop tumor cells from dividing so they stop growing or die, may kill more tumor cells.

PURPOSE: Phase II trial to study the effectiveness of reducing immunosuppression, and giving interferon alfa and combination chemotherapy, in treating patients who have malignant tumors that develop after organ transplant.

OBJECTIVES: I. Evaluate the complete remission rate and survival of patients with lymphoproliferation following organ transplantation treated with a defined sequential approach: modification of immunosuppression, with surgery or limited radiotherapy for an isolated site of disease; interferon alfa; and chemotherapy (ProMACE-CytaBOM; cyclophosphamide, doxorubicin, etoposide, prednisone, cytarabine, bleomycin, vincristine, methotrexate).

OUTLINE: All patients receive modification of immunocompetence, unless rejection is present at outset. These patients proceed directly to interferon treatment. Group 1 (see Disease Characteristics): Patients receive reduced doses of their current immunosuppressive therapy for 10 days. Group 2: Patients receive reduced doses of some of their current immunosuppressive therapy and discontinue some of the other therapy for 14 days. Immunosuppressive therapy then resumes on day 15. Immunosuppressive therapy continues throughout other therapy, unless otherwise noted. Some patients may then undergo surgery or radiotherapy. Interferon therapy: Patients receive interferon alfa (IFNA) subcutaneously or intramuscularly on days 1-28 for a maximum of 3 courses. Patients then receive maintenance therapy with IFNA 3 days a week for 4 weeks for up to 6 courses. Chemotherapy (ProMACE-CytaBOM): Immunosuppressive therapy is stopped on days 1-20. Patients receive cyclophosphamide IV, doxorubicin IV, and etoposide IV over 60 minutes on day 1, oral prednisone on days 1-14, and cytarabine IV, bleomycin IV, vincristine IV, and methotrexate IV on day 8. Treatment is repeated every 21 days for up to 6 courses. Patients with positive CSF cytology receive intrathecal methotrexate or cytarabine on days 1, 3, 5, 7, and 14. Some patients may continue this therapy on day 21 , then every 3 weeks for 5 doses, or may receive cranial irradiation. Patients are followed monthly for 1 year, every 2 months for 1 year, every 4 months for 1 year, then every 6 months thereafter.

PROJECTED ACCRUAL: A total of 50 patients will be accrued for this study within 4-5 years.

DISEASE CHARACTERISTICS: Histologically proven lymphoproliferation following organ (kidney, liver, or heart) allograft Bidimensionally measurable disease If all disease removed at biopsy, eligible only if recurrence is bidimensionally measurable Group 1 (clinically urgent disease): Histologically proven involvement of the allograft OR Histologically proven bone marrow involvement OR Liver involvement with hepatic insufficiency Bilirubin greater than upper limit of normal (ULN) OR SGOT or SGPT at least 2 times ULN OR Clinical hepatic encephalopathy OR LDH at least 3 times ULN OR Systemic sepsis OR Locally urgent lesions Tonsillar enlargement that threatens airway Superior vena cava syndrome Bilateral hydronephrosis Postobstructive pneumonia OR Small noncleaved lymphocytic lymphoma (i.e., adult Burkitt's lymphoma) Group 2: All other patients No CNS disease only

PATIENT CHARACTERISTICS: Age: 15 and over Performance status: Not specified Hematopoietic: Not specified Hepatic: See Disease Characteristics Renal: Not specified Cardiovascular: See Disease Characteristics Pulmonary: See Disease Characteristics Other: No known AIDS, HIV-associated complex, or positive HIV antibody No other malignancy within past 5 years, except: Adequately treated basal or squamous cell skin cancer Adequately treated stage I or II cancer or other noninvasive cancers Carcinoma in situ of the cervix Not pregnant or nursing Fertile patients must use effective contraception

PRIOR CONCURRENT THERAPY: Biologic therapy: No prior interferon for lymphoma No prior bone marrow transplantation Chemotherapy: No prior chemotherapy for lymphoma Endocrine therapy: Not specified Radiotherapy: Not specified Surgery: See Disease Characteristics Other: Intra-aortic balloon pump allowed only for heart failure caused by acute rejection or lymphomatous involvement