Stem cell transplant or rescue: patient has not had a prior stem cell transplant or rescue No prior treatment with high-dose chemotherapy (defined as treatment utilizing stem cell rescue) Patient must be >= 3 months since high dose chemotherapy and peripheral blood stem cell rescue prior to registration Previous high-dose chemotherapy requiring stem cell rescue. Must not be eligible for high-dose therapy with autologous stem cell transplantation rescue Prior high dose chemotherapy requiring stem cell rescue. Histologically confirmed non-Hodgkin lymphoma and be considered ineligible for standard curative therapeutic options, including high dose chemotherapy with autologous stem cell rescue Previous high-dose chemotherapy requiring allogenic stem cell rescue. Patients who have received any of the following:\r\n* > 2 chemotherapy regimens\r\n* Myeloablative chemotherapy with stem cell rescue\r\n* Craniospinal irradiation Previous high-dose chemotherapy requiring stem cell rescue Eligible for high-dose therapy and autologous stem-cell rescue Comorbid condition(s) which, in the opinion of the attending physician and/or MSK Cancer Center (CC) principal investigator, will preclude stem cell mobilization and/or high-dose therapy with autologous stem cell rescue Meets standard eligibility requirements for high dose chemotherapy with autologous stem cell rescue (COHORT 1) or allogeneic hematopoietic stem cell transplant (COHORT 2) and has signed consent for those procedures Patients must have a minimum stem cell dose of 4x10^6 CD34+ MNC/kg stored for autologous stem cell rescue Treatment with high-dose chemotherapy and hematopoietic stem-cell rescue within 3 months prior to initiation of study drug High-dose chemotherapy with stem-cell rescue: interval >= 3 months before study enrollment Patients with multiple myeloma who are potential candidates for high dose chemotherapy with stem cell rescue Scheduled to receive stem cell rescue therapy in conjunction with study related course(s) of emetogenic chemotherapy Frequent use of rescue opioids > 8 x/day or rescue bronchodilators > 8 x/day over last 24 hours Approved rescue medication for the treatment of nausea and vomiting is permitted at the discretion of the investigator; the rescue antiemetics allowed will include: ondansetron, granisetron and lorazepam Will be receiving stem cell rescue therapy in conjunction with study-related course of emetogenic chemotherapy or during the 14 days following administration of fosaprepitant/placebo for fosaprepitant Patients with a history of organ transplant including high dose chemotherapy with autologous stem cell rescue