The purpose of this study is to test what effects 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. Participants will receive one pre-transplant vaccine dose 7-30 days before stem cell collection. Patients will then be given a G-CSF stimulating factor. A second vaccine dose will be given between day 20-34 after transplant. All patients will be co-immunized with Prevnar 13 at the time they receive the survivin vaccine. The study will enroll 10 patients who can be either newly diagnosed patients or those who have relapsed or become refractory to standard myeloma medications. To learn more, click the button below: Survivin Vaccine Plus Auto Transplant