A Study of Romosozumab in Women With Multiple Myeloma and Osteoporosis

Inclusion Criteria: * Documented MM per International Myeloma Working Group diagnostic criteria (evidence of myeloma defining event attributed to underlying plasma cell disorder): i. Clonal plasma cells in the bone marrow ≥ 10% or presence of a biopsy proven plasmacytoma; and ii. Any one or more of the following myeloma defining events: * Evidence of end organ damage that can be attributed to the underlying plasma cell proliferative disorder: 1. Hypercalcemia: serum calcium \>0.25 mmol/L (\>1 mg/dL) higher than the upper limit of normal or \>2.75 mmol/L (\>11 mg/dL) 2. Renal insufficiency: creatinine clearance \< 40 mL/min or serum creatinine 177µmol/L (\>2 mg/dL) 3. Anemia: hemoglobin \> 2 g/dL below the lower limit of normal, or a hemoglobin value \<10 g/dL 4. Bone lesions: one or more osteolytic lesions on skeletal radiography, CT, or PET/CT * Clonal bone marrow plasma cell percentage ≥ 60%; or * Involved: uninvolved serum free light chain (FLC) ratio ≥ 100 (involved FLC level be ≥ 10 mg/dL; or * \>1 focal lesion on MRI studies (at least 5 mm in size) * Presence of lytic bone lesion(s) due to MM based on radiographic evidence with at least one measurable lesion (≥0.5 cm in its largest diameter by computerized tomography \[CT\]) * Postmenopausal female, defined as last menstrual cycle at least 12 months prior to study enrollment * Must have one of the following: * osteoporosis on dual X-ray absorptiometry (DXA) scan; or * fragility fracture of the spine or hip; or * morphometric spine fracture; or * osteopenia with elevated risk of fracture (calculated by the FRAX online calculator) * Within 12 months prior to study entry, ≤ 4 doses of prior intravenous (IV) bisphosphonate with the last dose ≥ 3 months prior to study entry. * Prior oral bisphosphonates are allowed if the last dose was ≥ 3 months prior to study entry. * Prior denosumab use is allowed for the following: * For patients who received ≤ 5 consecutive doses of denosumab with the last dose of denosumab received ≥ 3 months prior to study entry. * For patients who received ≥ 6 doses of denosumab, IV bisphosphonate should be given at least 1 month after the last dose of denosumab (if the last dose of denosumab was within the past 2 years). Patients are then eligible ≥ 3 months after IV bisphosphonate is received. If ≤ 2 years have elapsed since the last dose of denosumab, IV bisphosphonate is not required, and patients are eligible for the study. * Signed informed consent form(s). Individuals with impaired decision-making capacity may enroll if legally authorized representatives consent on behalf of individuals with impaired decision-making capacity. * Ability to comply with all study-related procedures in the investigator's judgment * 18 years of age or older Exclusion Criteria: * Assigned male at birth * Received teriparatide or other PTH analog use within 12 months prior to study entry * Receiving concurrent antiresorptive therapy * History of cardiovascular event (myocardial infarction and/or stroke) within the past 12 months of study entry * History of non-healed dental or oral surgery * History of osteonecrosis of the jaw * 25 (OH) vitamin D levels \< 20 ng/mL. Vitamin D repletion will be permitted and subjects may be rescreened once 25 (OH) vitamin D level ≥ 20 ng/mL. * Current hyper- or hypocalcemia, defined as albumin-adjusted serum calcium outside the normal range per institutional standard (\<8.5 or \>10.5 mg/dL).