This randomized open label clinical trial will evaluate the effect of continued denosumab alone over 18 months versus denosumab with added abaloparatide for 18 months. 70 postmenopausal women will be enrolled over a period of 18 months. The co-primary outcomes will be group differences in bone mineral density (BMD) of the total hip and lumbar spine at 18 months. Secondary outcomes will include group differences in bone mineral density (BMD) at the femoral neck, trochanter and wrist sites at 6, 12 and 18 months, spine and total hip bone mineral density (BMD) at 6 and 12 months and trabecular bone score (TBS) at 18 months. Secondary outcomes will also include within group changes from baseline for each of these variables. Bone turnover markers will also be measured to demonstrate that PINP levels will increase with administration of abaloparatide even in the setting of ongoing denosumab, while CTX levels will remain low.