Dose Augmented Rituximab and ICE for Pts With Primary Refractory and Poor Risk Relapsed Aggressive B-Cell NHL

Inclusion Criteria: * Histologic diagnosis of the one of the following B cell aggressive lymphomas, confirmed by an MSKCC pathologist: Diffuse Large, Immunoblastic, Mantle cell, Anaplastic Large Cell, De novo transformation of follicular lymphoma, or classical Hodgkin's lymphoma which is CD20 antigen positive. * Tumors must stain positive for CD20. * Primary refractory disease proven by biopsy or fine needle aspiration (cytology) of an involved site * Relapsed diffuse large, immunoblastic, anaplastic, de novo transformation of follicular lymphoma, or classical Hodgkin's lymphoma which is CD20 antigen positive proven by biopsy or fine needle aspiration (cytology) of an involved field site and at least two of the three following risk factors: LDH\> upper limit of normal, KPS \< 80%, Stage III or IV disease. * All mantle cell lymphoma patients in first relapse * Failure of doxorubicin or mitoxantrone containing front-line therapy * Bidimensionally measurable disease. * Cardiac ejection fraction of greater than 50%, measured since last chemotherapy. * Serum creatinine \<1.5 mg/dl; if creatinine \>1.5 mg/dl then the measured 12- or 24-hour creatinine clearance must be \>60 ml/minute. * ANC\>1000/µl and Platelets\>50,000/µl * Total bilirubin \< 2.0 mg/dl in the absence of a history of Gilbert's disease. * Females of childbearing age must be on an acceptable form of birth control. * Age between 18 and 72 * HIV I and II negative. * Patients or their guardians must be capable of providing informed consent. Exclusion Criteria: * Any lymphoma subtype other than those described among the inclusion criteria. * All patients with relapsed diffuse large, immunoblastic, anaplastic, de novo transformation of follicular lymphoma, or classical Hodgkin's lymphoma which is CD20 antigen positive disease who have \<2 of following risk factors: LDH\> upper limit of normal, KPS \< 80%, Stage III or IV disease. * History of second-line chemotherapy * Presence of CNS involvement. * Prior treatment with carboplatin, cisplatin, ifosfamide, or etoposide * Hepatitis B surface antigen positive. * Known pregnancy or breast-feeding. * Medical illness unrelated to NHL, which in the opinion of the attending physician and/or principal investigator will preclude administering chemotherapy safely. * History of any malignancy for which the disease-free interval is \<5 years, excluding curatively treated cutaneous basal cell or squamous cell carcinoma and carcinoma in-situ of the cervix