Ages =< years of age with hematologic diseases treatable by allogeneic HCT who through pre-existing medical conditions or prior therapy are considered to be at high risk for regimen related toxicity associated with a high dose transplant (> % risk of transplant-related mortality [TRM]); this criterion can include patients with a HCT-comorbidity index (CI) score of >= ; transplants should be approved for these inclusion criteria by the principal investigators at the collaborating centers and at Fred Hutchinson Cancer Research Center (FHCRC); all children < years must be discussed with the FHCRC principal investigator (PI) prior to registration Age-adjusted hematopoietic cell transplantation-comorbidity index (aaHCT-CI) less than or equal to . Patients >= age must have an comorbidity score (hematopoietic cell transplant-comorbidity index [HCT-CI]) =< (Sorror). The principal investigator is the final arbiter for comorbidity; Hematopoietic stem cell transplant comorbidity index (HCT-CI) >= ^ Ages =< years of age with hematologic diseases treatable by allogeneic HCT who through pre-existing medical conditions or prior therapy are considered to be at high risk for regimen related toxicity associated with a high dose transplant (> % risk of transplant related mortality [TRM]); this criterion can include patients with a hematopoietic cell transplant-comorbidity index (HCT-CI) score of > ; transplants should be approved for these inclusion criteria by the principal investigators at the collaborating centers and at Fred Hutchinson Cancer Research Center (FHCRC); all children < years must be discussed with the FHCRC principal investigator (PI) prior to registration Patients >= age must have a comorbidity score (hematopoietic cell transplant-comorbidity index [HCT-CI]) < (Sorror) > comorbidity points on the Hematopoietic Cell Transplant Co-Morbidity Index (HCT CI) Patients aged - with hematopoietic cell transplant-co-morbidity index (HCT-CI) of - are eligible Patients with comorbidity score > ; the principal investigator is the final arbiter of eligibility for comorbidity score > Patients >= and =< years of age may be eligible if they have a Hematopoietic Cell Transplantation- Comorbidity Index (HCT-CI) Co-Morbidity score =< HCT-CI/age score =< points (patients with greater than points will be allowed for trial with approval of the PI and the co-PI or his designee; this is an adjustment to account for healthy patients who meet the spirit of this protocol but have histories that result in higher than HCT-CI points HCT-CI/age score > points (patients with greater than points will be allowed for trial with approval of the principal investigator and the co-principal investigator or his designee; this is an adjustment to account for healthy patients who meet the spirit of this protocol but have histories that result in higher than HCT-CI points at least grade CIRS-G comorbidity (if compatible to participation in the study). PART : Comorbidity Index < at the time of pre-transplant evaluation Hematopoietic cell transplantation (HCT) co-morbidity index score > ; the principal investigator is the final arbiter of eligibility for comorbidity score > Hematopoietic Cell Transplantation-Specific Comorbidity Index score (HCT-CI) =< for patients in Cohort and > for Cohort Patients < age years must have a Karnofsky performance status (KPS) of >= % and a hematopoietic cell transplant comorbidity index (HCT-CI) score of or less Patients aged to years must have a KPS of >= % and an HCT-CI score of or less Patients aged to years must have a KPS of % and an HCT-CI score of or less Patients aged years or more must have a KPS of % and an HCT-CI score of or less Patients must have adequate Karnofsky performance status (KPS) and hematopoietic cell transplantation comorbidity index (HCT-CI) scores:\r\n* Patients < age years must have a KPS of >= % and an HCT-CI score of or less\r\n* Patients aged to years must have a KPS of >= % and an HCT-CI score of or less\r\n* Patients aged to years must have a KPS of % and an HCT-CI score of or less\r\n* Patients aged years or more must have a KPS of % and an HCT-CI score of or less Age >= years AND/OR Charlson comorbidity index score >= (prostate cancer diagnosis does not contribute to total score) Patients > must have Karnofsky performance score >= or ECOG - and comorbidity index < Age ? years with HCT comorbidity index < Severe, active comorbidity, including any of the following: Patients > to =< years: Karnofsky >= or ECOG - and non-age adjusted comorbidity index =< Significant comorbidity associated with an estimation of < remaining life years Patients must have a contraindication to cisplatin as defined in the following bullet points; sites must complete the online tool at comogram.org prior to step registration to determine if the patient is eligible; the scores must be recorded on a case report form (CRF)\r\n* Age >= with moderate to severe comorbidity or vulnerability to cisplatin, defined as having any one of the following conditions within days prior to step registration:\r\n** Modified Charlson Comorbidity Index >= \r\n** Adult Comorbidity Evaluation (ACE)- Index >= \r\n** Generalized Competing Event Model for Cancer Risk (GCE) omega PFS score < . \r\n** Geriatric screening (G-) score =< \r\n** Cancer and Aging Research Group (CARG) toxicity score >= %\r\n** Cumulative Illness Rating scale for Geriatrics (CIRS-G) score >= OR\r\n* Age < with severe comorbidity or vulnerability to cisplatin, defined as having two or more of the following conditions within days prior to step registration \r\n** Modified Charlson Comorbidity Index >= \r\n** ACE- Index >= \r\n** GCE omega PFS-score < . \r\n** G- score =< \r\n** CARG Toxicity score >= %\r\n** CIRS-G score >= OR\r\n* Age >= with an absolute or relative contraindication to cisplatin, defined as one or more of the following within days prior to Step registration:\r\n** Creatinine clearance (CC) > and < cc/min; for this calculation, use the Cockroft-Gault formula\r\n** Zubrod performance status prior to step registration\r\n** Pre-existing peripheral neuropathy grade >= \r\n** History of hearing loss, defined as either: \r\n*** Existing need of a hearing aid OR \r\n*** >= decibel shift over contiguous frequencies on a pretreatment hearing test Comorbidity or incurrent illness Charlson index of comorbidity score =< Comorbidity that would interfere with therapy Ineligible for intensification treatment due to age or significant comorbidity > comorbidity points on the Hematopoietic Cell Transplantation-Specific Comorbidity Index (HCT-CI) Patients >= years: comorbidity score of or higher Ages =< years of age with hematologic diseases treatable by allogeneic HCT who through pre-existing medical conditions or prior therapy are considered to be at high risk for regimen related toxicity associated with a high dose transplant (> % risk of transplant related mortality [TRM]); this criterion can include patients with a HCT-comorbidity index (CI) score of >= ; transplants should be approved for these inclusion criteria by the principal investigators at the collaborating centers and at the Fred Hutchinson Cancer Research Center (FHCRC); all children < years must be discussed with the FHCRC principal investigator (PI) prior to registration Hematopoietic Cell Transplantation Specific Comorbidity Index (HCT-CI) < for age < , HCT-CI < for age > History of uncontrolled depression or other psychiatric comorbidity with psychosis Underlying structural brain abnormality or neurologic comorbidity. Subject has a modified hematopoietic cell transplant comorbidity index (HCT-CI) score ? Active infection or chronic comorbidity that would interfere with therapy