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.

Some women on denosumab treatment for osteoporosis remain at high risk for fracture. These include women who sustain incident fractures on denosumab and those who have declining bone mineral density (BMD) or persistently low bone mineral density (BMD), despite treatment. There are few options available for these patients. Denosumab withdrawal is associated with dramatic increased bone remodeling, rapid prominent bone loss, and multiple vertebral fractures (Cummings JBMR 2017). Switching from denosumab to teriparatide is associated with substantial BMD loss in the hip and femoral neck. After 2 years of denosumab treatment, when women are switched to teriparatide, total hip BMD remains below the baseline (at end of denosumab treatment) over the entire 2 years of teriparatide treatment (Leder Lancet 2015).

Abaloparatide might be a better option than teriparatide in patients switching from denosumab, because it is less pro-resorptive than teriparatide, however, hip BMD will still likely decline. Alternatively, adding abaloparatide to ongoing denosumab might be an excellent treatment option for these women. One of the investigators has previously shown that adding teriparatide to ongoing alendronate results in improved BMD and bone strength, compared to switching to teriparatide (Cosman JCEM 2009 and Cosman JBMR 2013). Others have shown that co-administration of teriparatide and denosumab to treatment naïve women increases BMD more than either agent alone (Tsai Lancet 2013, Leder et al JCEM 2014). Based on both of these observations, the investigators believe that adding abaloparatide to continued denosumab treatment will allow bone formation to increase, without increasing bone resorption (modeling-based bone formation) and will produce substantial BMD increments in both spine and hip.

Hypothesis: In women who still appear to be at high risk for fracture while receiving ongoing denosumab therapy, adding abaloparatide will increase BMD of the lumbar spine and total hip significantly more than continuing denosumab alone.

Inclusion Criteria:

• postmenopausal woman >age 45 of any racial origin
• Participants will have received at least 4 prior denosumab treatments and be within 7 months from their last denosumab injection
• Participants are willing to participate for the duration of the study and have no physical or psychological illness that would prohibit them from participating.
• Diagnosis of osteoporosis based on bone mineral density and/or fracture criteria. Osteoporosis will be defined by bone mineral density T-Score < -2.5 at lumbar spine (at least 2 evaluable vertebrae between L1 and L4), total hip or femoral neck. Osteoporosis will also be defined clinically in women with osteoporotic fractures within the preceding 5 years, including clinical vertebral or nonvertebral fractures or vertebral fracture confirmed by radiograph or lateral DXA VFA image, along with a DXA BMD T-Score < -1.5 at one or more skeletal sites.

Exclusion Criteria:

• Use of drugs other than denosumab (within the preceding 3 months) known to affect skeletal or calcium homeostasis.
• Fewer than 2 evaluable lumbar vertebrae
• A history of a symptomatic renal stone within the past 2 years or history of multiple symptomatic renal stones within the preceding 10 years
• Skeletal Disorders other than osteoporosis, including hypercalcemia, hyperparathyroidism, or Paget's Disease
• History of external or internal radiation therapy
• Estimated GFR below 30 ml/min
• Any contraindications to receipt of Abaloparatide or Denosumab
• History of any cancer in past 5 years (except basal/squamous skin cancer)
• Unexplained elevation of Serum Alkaline Phosphatase
• History of atypical femoral fracture