Study of Plinabulin and Pegfilgrastim in People With Multiple Myeloma Undergoing an Autologous Hematopoietic Stem Cell Transplant (AHCT)

Inclusion Criteria: * Histologic confirmation of multiple myeloma by the enrolling institution in patient undergoing autologous HCT with melphalan 140 or 200 mg/m\^2 * Age 18-75 * Have at least 3 x 10\^6 CD34+ autologous stem cells/kg to be infused * Karnofsky performance greater than or equal to 60 within 2 weeks prior to enrollment. * Organ function testing within 28 days before enrollment: 1. LVEF ≥45% by MUGA or rest ECHO 2. Diffusion capacity \>45% (adjusted for hemoglobin) as predicted by pulmonary function testing * Clinical laboratory values meeting the following criteria within 14 days before enrollment: 1. Platelet count ≥ 20 x 109/L 2. ALT and AST ≤ 2.5 x ULN 3. Total bilirubin ≤ 2.5 x ULN; except if the elevation is due to Gilbert's syndrome 4. Calculated creatinine clearance \> 40 mL/min * All women of childbearing potential must: 1. Have a negative serum pregnancy test (β-human chorionic gonadotropin \[β-hCG\]) within 14 days prior to enrollment (and pre-AHCT per institutional guidelines) 2. For 180 days after receiving plinabulin practice a highly effective method of birth control consistent with local regulations regarding the use of birth control methods for subjects participating in clinical studies: e.g., established use of oral, injected or implanted hormonal methods of contraception; placement of an intrauterine device (IUD) or intrauterine system (IUS); barrier methods: condom with spermicidal foam/gel/film/cream/suppository or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository; male partner sterilization (the vasectomized partner should be the sole partner for that subject); true abstinence (when this is in line with the preferred and usual lifestyle of the subject) 3. For 180 days after receiving plinabulin, a woman must agree not to donate eggs (ova, oocytes) for the purposes of assisted reproduction 4. Not of childbearing potential is defined as postmenopausal (\>45 years of age with amenorrhea for at least 12 months or any age with amenorrhea for at least 6 months and a serum follicle stimulating hormone (FSH) level \>40 IU/mL); permanently sterilized (e.g., tubal occlusion, hysterectomy, bilateral salpingectomy); or otherwise be incapable of pregnancy 5. Note: If the childbearing potential changes after start of the study (e.g., woman who is not heterosexually active becomes active) a woman must begin a highly effective method of birth control, as described above. * A man who is sexually active with a woman of childbearing potential and has not had a vasectomy must agree to use a barrier method of birth control e.g., either condom with spermicidal foam/gel/film/cream/suppository or partner with occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/suppository, and all men must also not donate sperm for 180 days after receiving plinabulin Exclusion Criteria: * Other malignancy within the past 2 years, except for the following if treated and not active: basal cell or nonmetastatic squamous cell carcinoma of the skin, cervical carcinoma in situ or International Federation of Gynecology and Obstetrics (FIGO) Stage 1 carcinoma of the cervix * Clinically significant infection, including known HIV or hepatitis C infection, or known hepatitis B (Hep B) surface antigen positivity. Patients with Hep B Core Antibody positivity can be enrolled if the Hep B PCR is negative, and they are on antiviral suppression. * Patients with uncontrolled systemic fungal, bacterial, viral, or other infection despite appropriate treatment at the time of enrollment. * Received an investigational drug (including investigational vaccines) or used an invasive investigational medical device within 14 days or 5 half-lives before enrollment * Had hospitalization for infection or major surgery (e.g., requiring general anesthesia) within 14 days before enrollment or have not fully recovered from surgery. Note: subjects with surgical procedures conducted under local anesthesia may participate * A woman who is pregnant or breast-feeding, or a woman who is planning to become pregnant or a man who plans to father a child while enrolled in this study or within 180 days after plinabulin * Uncontrolled medical, psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol, as judged by the PI; or unwillingness or inability to follow the procedures required in the protocol. * Significant cardiovascular history: * History of myocardial infarction or ischemic heart disease within 1 year (within a window of up to 18 days less than 1 year) before study drug administration * Uncontrolled arrhythmia * History of congenital QT prolongation * Electrocardiogram (ECG) findings consistent with active ischemic heart disease * New York Heart Association Class III or IV cardiac disease; * Uncontrolled hypertension: blood pressure consistently \>150 mm Hg systolic and \> 100 mm Hg diastolic in spite of antihypertensive medication * Prior transient ischemic attack or cerebrovascular accident with in the past year (within an 18-day window). Any neurologic toxicities ≥ Grade 2 within 3 weeks of randomization. * History of hemorrhagic diarrhea, inflammatory bowel disease or active uncontrolled peptic ulcer disease. (Concomitant therapy with ranitidine or its equivalent and/or omeprazole or its equivalent is acceptable). History of ileus or other significant gastrointestinal disorder known to predispose to ileus or chronic bowel hypomotility. * Known prior hypersensitivity reaction to any product containing polysorbate 80, polyoxyethylene 15-hydroxystearate/Macrogol 15 hydroxystearate (Solutol HS 15/Kolliphor HS 15). * Any medical conditions that, in the Investigator's opinion, would impose excessive risk to the patient. Examples of such conditions include uncontrolled diabetes, infection requiring parenteral anti-infective treatment, liver failure, any altered mental status or any psychiatric condition that would interfere with the understanding of the informed consent form. * Unwilling or unable to comply with procedures required in this protocol.