Using Romiplostim to Treat Low Platelet Counts Following Chemotherapy and Autologous Hematopoietic Cell Transplantation in People With Blood Cancer

Inclusion Criteria: * Adult patients ≥ 18 years old diagnosed with multiple myeloma (MM), any subtype of Hodgkin lymphoma (HL), or any subtype of non-Hodgkin lymphoma (NHL) * For MM, the conditioning regimen used will be high-dose melphalan.°For HL and NHL, the conditioning will be one of the following high-dose regimens: BEAM, CBV, or TBC. * Other conditioning regimens not listed above, or variations of the above conditioning regimens, may be allowed at the discretion of the principal investigator if the regimen is considered myeloablative. * Adequate organ function is required, defined as follows: * Serum bilirubin ≤ 2 mg/dL, unless benign congenital hyperbilirubinemia. * AST, ALT, and alkaline phosphatase \< 3 times the upper limit of normal. * Creatinine clearance ≥ 40 ml/min (calculated by Cockcroft Gault) * LVEF ≥ 45% by MUGA or resting echocardiogram * Pulmonary function (FEV1 and corrected DLCO) ≥ 45% predicted. * Adequate performance status ECOG ≤ 2. * Ability to provide written informed consent. * Patients undergoing HDT-AHCT. Exclusion Criteria: * Patients with a previous diagnosis of a myeloid malignancy. * Patients for whom the treating oncologist will be using a non-standard platelet transfusion threshold during the AHCT. * Patients with a history of a prior symptomatic or incidental venous thromboembolic event (such as DVT or pulmonary embolism) within the prior 6 months are eligible if they are on and tolerating anti-coagulation, or greater than 6 months ago are eligible if they completed or are on and tolerating anti-coagulation. °A venous thrombotic event associated with a central venous catheter will not make the patient ineligible. * Patients with a history of symptomatic arterial thrombotic events such as myocardial infarction, ischemic cerebral vascular accident or transient ischemic attack in the past 6 months are ineligible. * Patients who had been diagnosed with Immune Thrombocytopenic Purpura (ITP) at any time prior to the AHCT are ineligible. * Patients with a serious concomitant medical condition that could interfere with the conduct of the clinical trial, such as unstable angina, renal failure requiring hemodialysis, or active infection requiring IV antibiotics. * Previous use of romiplostim, PEGylated recombinant human megakaryocyte growth and development factor, eltrombopag, recombinant human TPO, any other TPO receptor agonist, or any investigational platelet producing agent. * Females who are pregnant or breastfeeding or planning to become pregnant or breastfeed during treatment and for an additional 30 days after treatment discontinuation or longer if required by prescribing information for chemotherapy received during the study. * Patients unwilling to use highly effective contraception during the study period and for the duration required by prescribing information for chemotherapy(ies) administered during the study.