Patients must not have testicular involvement; if clinical or ultrasound findings are equivocal, biopsy must be performed; all tests for establishing testicular involvement must be completed within days prior to registration Paranasal sinus/nasal cavity malignancy is considered unresectable with negative margins surgery or resection would be considered excessively morbid; this could include lesions with:\r\n* Carotid involvement\r\n* Cavernous sinus invasion\r\n* Brain invasion\r\n* Orbital apex\r\n* Intraconal space\r\n* Pterygoid musculature involvement\r\n* Invasion of the clivus Leptomeningeal involvement of cancer Patients must be without evidence of visceral or bone involvement with metastatic cancer on physical exam or any diagnostic study; extensive nodal involvement is allowed Tumor involvement > % of the liver NOTE: these requirements do not apply to those with marrow involvement of lymphoma (any extent) Oligometastatic disease sites not eligible based on concern for toxicity: \r\n* Trachea involvement (direct invasion, tumors close to or abutting trachea are eligible)\r\n* Heart (direct invasion or involvement, pericardial lymph nodes can be treated) Oligometastatic disease sites not eligible: \r\n* Trachea involvement (direct invasion, tumors close to or abutting trachea are eligible)\r\n* Heart (direct invasion or involvement, pericardial lymph nodes can be treated) Patients with carotid artery involvement or encasement will be allowed provided they have no symptoms related to carotid involvement Exhibits clinical signs of meningeal involvement of MM Known amyloid involvement Isolated sclerosing cholangitis without evidence of active hepatic LCH as the only evidence of risk organ involvement. Absolute neutrophil count >= /mm^ within days prior to initiation of therapy. (Patients with documented marrow involvement (with lymphoma) or hypersplenism secondary to involvement of the spleen by lymphoma at the time of randomization are not required to meet the parameter). Platelet count >= K /mm^ within days prior to initiation of therapy. (Patients with documented marrow involvement (with lymphoma) or hypersplenism secondary to involvement of the spleen by lymphoma at the time of randomization are not required to meet the parameter). Serum creatinine =< . mg/dL or creatinine clearance of > ml/min within days prior to initiation of therapy. (Patients with documented marrow involvement (with lymphoma) or hypersplenism secondary to involvement of the spleen by lymphoma at the time of randomization are not required to meet the parameter). Total bilirubin =< . mg/dL within days prior to initiation of therapy. (Patients with documented marrow involvement (with lymphoma) or hypersplenism secondary to involvement of the spleen by lymphoma at the time of randomization are not required to meet the parameter). Tumor > . cm, nodal involvement, or metastatic involvement Objective measurable (cardiac, renal or liver) organ amyloid involvement defined as follows (amyloid involvement of at least required):\r\n* Mean wall thickness > mm on echocardiogram, with no other cardiac cause or an elevated N-terminal pro b-type natriuretic peptide (NT-ProBNP) (> ng/L) in the absence of renal failure or atrial fibrillation\r\n* Renal involvement is defined as proteinuria (predominantly albumin) > . g/day in a -hour urine collection\r\n* Total liver span > cm in the absence of heart failure or alkaline phosphatase > . times institutional upper limit of normal (ULN)\r\n* NOTE: Amyloid involvement of other organ systems is allowed, but not required No clinical or pathologic evidence of nodal involvement Patients with diffuse/multifocal liver involvement are eligible Unless considered to be due to leukemic organ involvement. Leptomeningeal involvement regardless of treatment status Leptomeningeal involvement regardless of treatment status Parenchymal brain involvement with lymphoma A minimum tissue requirement of >= core biopsies with tumor involvement and at least % tumor involvement in one of the core biopsies is required Patients with metastatic central nervous system (CNS) tumors are allowed provided that they are clinically stable for a period of days prior to study entry and there is not a requirement for steroid (other than close to physiologic doses) or anti-convulsant therapy; patients with leptomeningeal involvement are excluded Surgical Stage III disease includes those patients with positive adnexa, parametrial involvement, tumor invading the serosa, positive pelvic and/or para-aortic nodes, or vaginal involvement. Evidence of nodal involvement identified in the operating room (OR) Multifocal progression or involvement of the leptomeninges Skin involvement. Persistent marrow involvement (> %) with HL after salvage cytoreductive therapy and before stem cell mobilization Serum bilirubin < . mg%, regardless of whether patients have liver involvement secondary to tumor Known leptomeningeal involvement. Clinical signs of brain involvement or leptomeningeal disease Known meningeal involvement of MM. Patients must be without evidence of visceral or bone involvement with metastatic cancer on physical exam or any diagnostic study; extensive nodal involvement is allowed Radiographic or cytologic evidence of diffuse leptomeningeal extension - tumors with limited subependymal involvement are eligible Total bilirubin =< . institutional upper limit of normal (ULN), unless elevated secondary to lymphomatous involvement of liver or biliary system, or due to other HIV medications (e.g., indinavir, tenofovir, or atazanavir); for direct bilirubin > . due to hepatic involvement by tumor for the initial dose of EPOCH drug adjustment Objective, measurable major (cardiac or renal) organ amyloid involvement as defined as follows (amyloid involvement of at least required): Cardiac involvement is defined as the presence of a mean left ventricular wall thickness on echocardiogram greater than mm in the absence of other potential causes of left ventricular hypertrophy (controlled hypertension is allowed) with a noncardiac biopsy showing amyloid, or a positive cardiac biopsy in the presence of clinical or laboratory evidence of involvement. If there is isolated cardiac involvement, then typing of amyloid deposits is recommended. Renal involvement is defined as proteinuria (predominantly albumin) >. g/day in a -hour urine collection. Note: Amyloid involvement of other organ systems is allowed, but not required. Patients are excluded if they have known involvement of melanoma within the gastrointestinal tract involvement of pterygopalatine fossa, maxillary sinus, or facial skin;. sphenoid bone or foramen ovale involvement; Patients with known cerebral or meningeal involvement by lymphoma are excluded Known amyloid involvement Tumors with involvement of the mediastinum. PHASE II: Patients must be without evidence of visceral or bone involvement with metastatic cancer on physical exam or any diagnostic study; extensive nodal involvement is allowed Any lymph node involvement that results in % cellularity or greater regardless of primary tumor site involvement (includes no residual disease in the breast). Patients must be without visceral or bone involvement with metastatic breast cancer on physical exam or any diagnostic study; patients with extensive nodal involvement classified as stage IV disease, are eligible Patients with documented marrow involvement by lymphoma at the time of registration are not required to meet the above hematologic parameters Patients with nodal involvement are eligible At least one of the following indications for therapy:\r\n* Pulmonary involvement\r\n* Visceral involvement\r\n* Pain\r\n* Edema\r\n* Substantial lymph node involvement\r\n* Ulcerating lesions\r\n* Decreased range of joint motion due to KS\r\n* Multiple lesions not amenable to local therapy\r\n* Significant psychological impact leading to social withdrawal Cardiac involvement Known symptomatic brain mets or leptomeningeal involvement Patient has Grade B aGvHD with skin-only involvement. Cardiac involvement Subjects with negative metastatic involvement (M). Osteolysis of a vertebral body(ies) with or without fracture at a site of metastatic infiltration/multiple myeloma, that poses risk of impending vertebral collapse; this is detected by the following cross-sectional imaging (MRI or CT) conditions:\r\n* In the thoracic spine: \r\n** A >= % involvement of the vertebral body with no destruction of other structures or;\r\n** A >= % involvement of the vertebral body associated with costovertebral joint destruction or posterior elements involvement\r\n* In the lumbar spine: \r\n** A >= % involvement of the vertebral body with no destruction of other structures or;\r\n** A >= % involvement of the vertebral body associated with involvement of posterior elements Evidence of cardiac involvement by echocardiography with an end-diastolic interventricular septal wall thickness > mm, Presence of less than % liver involvement by cancer Presence of clinically evident active CNS metastases, including leptomeningeal involvement, requiring steroid or radiation therapy Presence of clinically evident active CNS metastases, including leptomeningeal involvement, requiring steroid or radiation therapy Brain stem involvement allowed Radiologic suspicion of lung involvement (primary or metastatic), lymphangitic carcinomatosis, or airway involvement secondary to tumor infiltration. Plastic surgery involvement for oncoplastic reconstruction Clinical or radiologic history of lung/pleural involvement (primary or metastatic), lymphangitic carcinomatosis or airway involvement secondary to tumor infiltration Patients with endobronchial involvement seen on chest CT Patients with a grade / tumors and evidence of deep myometrial invasion or cervical involvement on preoperative imaging or physical exam