The purpose of this study is to test what effects (good and bad) a new cancer vaccine will have on participants and their cancer, when administered before and after their autologous hematopoietic cell transplant (HCT).

The name of the vaccine is called Dendritic Cell Survivin Vaccine (DC:AdmS). The vaccine is made using the participant's own blood cells. The vaccine will contain a virus called an adenovirus, similar the virus that causes the common cold. The virus has been changed so it cannot infect humans and cause infections. The vaccine will be prepared at Moffitt Cancer Center in the Cell Therapy Laboratory Facility.

This study is designed to test the safety and efficacy of the survivin vaccine, as well as the biological activity. A total sample size of 30 patients will be used for the study. In the 1st stage, 10 patients will be used to evaluate the safety and futility of the vaccine. If it passes the 1st stage, investigators will enroll another 20 patients (as 2nd stage) to evaluate the efficacy. The two- stage experiment is based on Simon minmax two-stage design for efficacy. Vaccine will be administered in two stages. After the first survivin vaccination, participants will be mobilized with G-CSF and both in vivo-primed T cells and stem cells will be collected in the same apheresis (the graft). T cells and the CD34 progenitor cells will be transferred back to the participant at the time of autologous graft infusion. Participants will receive re-vaccination on, or near, day 21 after transplant.

Inclusion Criteria:

Screening:

• As of protocol Version 2 there is no "screening phase".Patients previously consented to the screening phase could still be eligible for treatment if consented for treatment, based upon the updated eligibility criteria.

Treatment:

• Patients with histologically confirmed Multiple Myeloma that are being considered for high dose chemotherapy and autologous stem cell transplant.
• Patients must have a bone marrow biopsy available, or one scheduled to be performed for a clinical indication so that survivin expression could be determined (note: survivin staining in tumor need not be resulted prior to enrollment or treatment as it is obtained for correlative science).
• Patients planned for treatment with high dose melphalan and autologous hematopoietic cell transplant (HCT).
• Complete blood count (CBC) with an absolute neutrophil count (ANC) >= 1,000/uL, hemoglobin >= 8.0 g/dL and platelet count >= 50,000/uL.
• Liver enzymes: total bilirubin less than or equal to 2 mg/dL (>2 mg/dL permitted if the patient has evidence of Gilbert's disease based upon prior bilirubin elevation or genetic testing); Aspartate Aminotransferase (AST) and Alanine Aminotransferase (ALT) less than 1.5 X the upper limit of normal (ULN).
• Signed informed consent form in accordance with institutional and federal law policies.

Exclusion Criteria:

Treatment:

• Patients with Complete Response (CR) or stringent CR after induction therapy as defined by International Response Criteria after most recent therapy.
• Patients with progressive disease at time of transplant.
• Pregnant or lactating woman (as evaluated by serum testing within 48 hours of administration of the first vaccine in women of child bearing potential).
• HIV infection confirmed by nucleic acid tests (NAT).
• Common variable immunodeficiency.
• Active central nervous system (CNS) malignancy.
• Active bacterial, fungal or viral infection.
• Prior history of allogeneic hematopoietic cell transplantation
• Prior malignancy within 5 years of enrollment excluding non-melanoma skin cancer or cervical carcinoma after curative resection, not requiring chemotherapy.
• History of severe allergy (e.g., anaphylaxis) to any component of Prevnar or any diphtheria-toxoid containing vaccine.