This is an, open-label, phase II study of SRT501, alone or in combination with bortezomib, in subjects with measurable Multiple Myeloma. Sixty-one (61) evaluable subjects, who fulfill the inclusion/exclusion criteria, will be enrolled in this study. Pharmacokinetic (PK) samples will be collected from a subset of 15 subjects to determine SRT501 plasma concentrations in this patient population. Subjects will sign the informed consent form prior to any study related procedures. If eligible, subjects will receive 5.0 g of SRT501 to be administered for 20 consecutive days in a 21 day cycle for a maximum of 12 cycles. SRT501 will be administered as an oral suspension product at the same time each morning (approximately 15-30 minutes following consumption of breakfast) on all dosing days. Safety assessments will be performed continuously throughout the cycle and these will be reviewed for all subjects at Day 21 of each cycle prior to subjects proceeding to the next cycle. SRT501 will not be administered on Day 21 of each cycle. Subjects will be assessed for efficacy and response of SRT501 at the end of every 2 cycles (6 weeks) of treatment. When necessary, a bone marrow biopsy and CT (or appropriate radiographic imaging) of the chest and abdomen/pelvis will be performed to confirm response. After the first two cycles of SRT501 treatment and review of the efficacy and response analysis, any subject who exhibits stable disease or better with SRT501 monotherapy may continue on SRT501 monotherapy (5.0 g/day) for an additional two cycles. If, after the first two cycles of SRT501 monotherapy, a subject exhibits PD, then that subject will receive bortezomib (1.3 mg/ m2 on Day 1, Day 4, Day 8, and Day 11 in a 21 day cycle) in conjunction with SRT501 (5.0 g/day). Bortezomib will be administered prior to SRT501 administration. If after two additional cycles of SRT501 monotherapy (4 cycles total), the subject exhibits a MR or better, they will remain on SRT501 (5.0 g/day) treatment until they are judged to have SD or PD. At the time the subject is judged to have SD or PD after receiving at least four cycles of SRT501 (5.0 g/day) monotherapy, then they may also receive bortezomib (1.3 mg/m2 on Day 1, Day 4, Day 8, and Day 11 in a 21 day cycle) in conjunction with daily SRT501 dosing. If at any point while a subject is receiving SRT501 and bortezomib the subject is assessed to have PD, then they will be removed from the study and will be required to undergo End of Study assessments/follow-up approximately 28 days (+/- 7 days) following the last dose of SRT501 or SRT501 and bortezomib.