This study is for patients that have multiple myeloma that has come back or relapsed and their condition indicates a procedure called an Autologous Hematopoietic Stem Cell Transplantation (AHSCT). AHSCT is a procedure when stem cells from bone marrow or blood are removed before high-dose chemotherapy. Afterwards, the removed stem cells are put back into the patient's body to form a new population of blood cells.

The high-dose chemotherapy administered before the AHSCT is called "Conditioning Therapy." The FDA has approved the use of the drug melphalan as a conditioning therapy. This research study will look at whether adding the study drug called carfilzomib will improve participant outcomes. Carfilzomib is considered investigational and is not approved by the FDA for the treatment of relapsed multiple myeloma.

This study is divided into two phases.

Phase I: Dose Escalation Phase:

The main purpose of Part I of this study is to examine the safety of the study drug, carfilzomib, and determine the safest amount of the study drug that can be given to subjects who have multiple myeloma. Subjects on this study will receive different dose levels of the study drug. If you are one of the first three subjects to receive the study drug, it will be at what is called the 'starting dose' for the study which is the lowest dose that is expected to be tolerated based on prior research. After the first set of participants receive the study drug, the study doctor will review their health to see how they are tolerating the treatment. This will decide if the study drug dosage will be increased or decreased for the next set of subjects who join the study. It is anticipated that 12- 18 participants will enroll in the Phase I portion of this study.

Phase II: Safety Confirmation Phase:

Once the study doctor has discovered the highest possible dose of study drug that subjects can tolerate, up to 28 more subjects may be enrolled at that dose level. The main purpose of the Phase II portion of the study is look at how effective the combination of carfilzomib and melphalan when given before your stem cell transplantation is in treating multiple myeloma. This expansion phase will also include evaluation of two single agent carfilzomib maintenance therapy regimens for patients without disease progression at day 100.

This is a phase 1/2a trial. Since this is an AHSCT conditioning regimen trial, only one cycle of therapy will be administered for each subject.

PHASE 1 The phase 1 component has a typical 3+3 design.

• Initially up to three subjects will be enrolled in each cohort starting at cohort 0 in the table below.
• If no dose limiting toxicity (DLT) is noted among the 3 initial subjects, 3 additional patients will be accrued at the subsequent cohort.
• If 1/3 subjects experience DLT, 3 additional subjects will be accrued at the cohort. If no additional DLT occur, accrual will continue at the subsequent cohort.
• If 2 or more subjects experience DLT in a given cohort, the dose will be considered higher than the maximum tolerated dose (MTD) and the immediately lower dose will be considered the MTD.
• If accrual is completed in cohort 4 with 0/3 or 1/6 DLT, the MTD will be considered "not reached" and cohort 4 will be expanded in the phase 2 of the trial.
• If 2 subjects experience DLTs in cohort 0, patients will be accrued in cohort -1, one subject at a time, with the subsequent subject only being accrued once the current subject has completed the DLT period (transplant day 30). The doses in cohort -1 will be considered the MTD if 0/3 or 1/6 subjects experience DLT.
• If ≥ 2 subjects experience DLT in cohort -1 the study will be interrupted without proceeding to phase 2a and the combination of carfilzomib and high dose melphalan will be considered too toxic.

PHASE 2 Once the MTD for the combination of carfilzomib and high dose melphalan with AHSCT is found, there will be expansion of the MTD cohort so that 28 individuals will be treated at the MTD of carfilzomib and high dose melphalan.

Screening - Subjects likely to meet eligibility criteria will be offered participation in the study after the investigator verifies with the registration system that there is a current available slot (phase 1). Subjects will sign informed consent prior to any protocol associated procedure. Screening procedures are outlined in Table 3 and will 1) ensure that subject meets all the eligibility criteria, 2) obtain disease assessment to allow efficacy measurements, 3) assess baseline toxicity and 4) provide initial biological samples for pharmacodynamic and correlative studies.

Treatment- Subjects will receive the appropriate dose of carfilzomib (according to assigned cohort in phase 1 and at the determined MTD in phase 2) on days -3 and -2. Carfilzomib will be infused over 30 minutes. On day -2, with 60 to 120 minutes of the end of infusion of carfilzomib, subjects will receive 200 mg/m2 of intravenous melphalan as an intravenous push or a fast infusion. Prophylaxis of chemotherapy induced nausea and vomiting will follow institutional guidelines.

Infusion of autologous cells- Infusion of autologous hematopoietic stem cells will occur on day 0 and follow institutional SOP.

Follow up phase - On day 1 following HSCT patients will receive pegfilgrastim 6 mg subcutaneously as per institutional standard of care aiming at faster engraftment. The follow up phase will last 100 days and will consist of standard post transplantation supportive care and monitoring of adverse events (AE's). For the phase 1 component of the study, dose-limiting toxicities will be captured during the first 30 days after transplantation (DLT period). Patients without progression may continue with carfilzomib maintenance therapy.

Patients will either be randomized in blocks of two to either maintenance therapy Arm 1= AB (two cycles of A followed by two cycles of B), or maintenance therapy Arm 2= BA (two cycles of B followed by two cycles of A). Maintenance regimen A will consist of carfilzomib 36 mg/m2 infused over 30 minutes on days 1,8,15. Maintenance regimen B will consist of carfilzomib 36 mg/m2 infused over 30 minutes on days 1, 2, 15 and 16. Each cycle will have 4 week duration. The first four maintenance therapy cycles will be dictated by a randomized assignment at time of study registration to maintenance therapy. For both maintenance therapy arms, a patient preference questionnaire will be administered to the patient upon completion of the 4th cycle. The remaining 8 cycles (cycles 5-12) will be administered according to the regimen schedule preferred by the patient as documented on the patient preference questionnaire.

Disease assessment- Disease assessment will occur at day 100 (+/- 7 days) and will consist of serum protein electrophoresis, serum and urine immunofixation, 24h urine protein electrophoresis, serum free light chains, bone marrow aspiration and biopsy, complete blood counts and metabolic panel.

Inclusion Criteria:

1. Age ≥ 18 years and ≤ 70 years

2. Life expectancy ≥ 12 months

3. Eastern Cooperative Oncology Group (ECOG) performance status 0-2

4. Diagnosis of symptomatic multiple myeloma, relapsed after initial therapy.

5. At least minimal response (defined as 25% decrease in the M protein in serum or urine) to the most recent treatment regimen.

6. Evaluable disease prior to most recent treatment regimen as defined by at least one of the following:

   • Serum monoclonal (M) protein ≥0.5 g/dl by protein electrophoresis

     • 200 mg of M protein in the urine on 24 hour electrophoresis

   • Serum immunoglobulin free light chain ≥10 mg/dL AND abnormal serum immunoglobulin kappa to lambda free light chain ratio

   • Monoclonal bone marrow plasmacytosis ≥30%

7. Adequate hepatic function, with serum ALT ≤ 3.5 times the upper limit of normal and serum direct bilirubin ≤ 2 mg/dL (34 µmol/L) within 14 days prior to start of therapy

8. Hemoglobin ≥ 8 g/dL (80 g/L) within 14 days prior to registration (subjects may be receiving red blood cell [RBC] transfusions in accordance with institutional guidelines)

9. Creatinine clearance (CrCl) ≥ 40 mL/minute within 14 days prior to registration, either measured or calculated using a standard formula (eg, Cockcroft and Gault).

10. Prior storage of at least 2 x 106 CD34+ cells/kg available for autologous transplantation. During the phase 1 component of the study, at least the same amount of cells is required as "back up" in the unlikely event of non-engraftment.

11. Subjects may have had a prior AHSCT for the treatment of MM as long as it was performed greater than 12 months from study registration.

12. Subjects must meet institutional general eligibility criteria for autologous transplantation.

13. Written informed consent in accordance with federal, local, and institutional guidelines.

14. Female of childbearing potential (FCBP) must agree to ongoing pregnancy testing and to practice contraception.

15. Male subjects must agree to practice contraception.

Exclusion Criteria:

1. Pregnant or lactating females.
2. Major surgery within 30 days prior to start of treatment.
3. Acute active infection requiring treatment (systemic antibiotics, antivirals, or antifungals) within 14 days prior to registration.
4. Known human immunodeficiency virus infection.
5. Active hepatitis B or C infection.
6. Unstable angina or myocardial infarction within 4 months prior to registration, NYHA Class III or IV heart failure, uncontrolled angina, history of severe coronary artery disease, severe uncontrolled ventricular arrhythmias, sick sinus syndrome, or electrocardiographic evidence of acute ischemia or Grade 3 conduction system abnormalities unless subject has a pacemaker.
7. Uncontrolled hypertension or uncontrolled diabetes within 14 days prior to registration.
8. Nonhematologic malignancy within the past 3 years with the exception of a) adequately treated basal cell carcinoma, squamous cell skin cancer, or thyroid cancer; b) carcinoma in situ of the cervix or breast; c) prostate cancer of Gleason Grade 6 or less with stable prostate-specific antigen levels; or d) cancer considered cured by surgical resection or unlikely to impact survival during the duration of the study, such as localized transitional cell carcinoma of the bladder or benign tumors of the adrenal or pancreas.
9. Significant neuropathy (Grades 3-4, or Grade 2 with pain) within 14 days prior to registration.
10. Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib).
11. Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days prior to registration.
12. Any other clinically significant medical disease or condition that, in the Investigator's opinion, may interfere with protocol adherence or a subject's ability to give informed consent.

Patients with relapsed multiple myeloma, candidates for autologous hematopoietic cell transplantation

12 months