Inclusion Criteria:

          -  Female patients must have a bone age of equal to or greater than 12 years of age as
             determined by local read of appropriate radiographic imaging

          -  Male patients must have a bone age of equal to or greater than 14 years of age as
             determined by local read of appropriate radiographic imaging

          -  Patients must have relapsed or become refractory to conventional therapy, with a
             regimen including some combination of high dose methotrexate, doxorubicin, cisplatin,
             ifosfamide and etoposide; and have had histologic verification of osteosarcoma at
             original diagnosis or at the time of recurrence

          -  Cohort 1 patients must have measurable disease according to Response Evaluation
             Criteria in Solid Tumors (RECIST) 1.1

          -  Cohort 2 patients must have had a complete resection of all sites of metastatic
             disease within 30 days prior to enrollment

               -  Patients will only be eligible after they have undergone complete surgical
                  resection of suspected metastatic disease that is histopathologically confirmed
                  to be osteosarcoma prior to enrollment

                    -  Note: the definition of complete resections is: gross resection of all
                       disease as per the operating surgeon; post-operative imaging is not required
                       for confirmation of complete resection

               -  Patients must undergo resection of any lung lesion meeting criteria for likely
                  metastatic disease, defined as:

                    -  3 or more lesions > 5 mm in diameter OR a single lesion > 1 cm

               -  Patients with lung as the only site of resected metastatic disease must have
                  refused participation in protocol AOST1421

                    -  Note: This applies if AOST1421 is open to enrollment at the enrolling
                       institution on the day the patient consents

          -  Patient must have adequate tumor specimen available for submission

          -  Patients must have a performance status corresponding to Eastern Cooperative Oncology
             Group (ECOG) scores of 0, 1 or 2; use Karnofsky for patients > 16 years of age and
             Lansky for patients =< 16 years of age

          -  Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70
             mL/min/1.73 m^2 or a serum creatinine based on age/gender as follows:

               -  Age: 11 to < 13 years old; 1.2 (male, female) maximum serum creatinine (mg/dL)

               -  Age: 13 to < 16 years old; 1.5 (male), 1.4 (female) maximum serum creatinine
                  (mg/dL)

               -  Age: >= 16 years old; 1.7 (male), 1.4 (female) maximum serum creatinine (mg/dL)

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN) for age

          -  Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase [AST]) or
             serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) < 2.5 x
             ULN for age

          -  Serum calcium or albumin-adjusted serum calcium >= 2.0 mmol/L (8.0 mg/dL) and =< 2.9
             mmol/L (11.5 mg/dL)

        Exclusion Criteria:

          -  Patients with known sensitivity to any of the products to be administered during the
             study (eg, mammalian derived products, calcium or vitamin D)

          -  Patients who are receiving other cancer directed therapy at the time of enrollment

          -  Patients who have previously received denosumab

          -  Patients who have previously received mithramycin, strontium-89, samarium-153 or
             rhenium

          -  Patients receiving bisphosphonates

          -  Pre-existing conditions

               -  Disorders associated with abnormal bone metabolism

               -  Hypocalcemia that is not corrected with oral calcium supplementation

               -  Vitamin D < 20 mg/mL

               -  Paget's disease

               -  Prior history or current evidence of osteonecrosis of the jaw

               -  Any dental or oral condition likely to result in disruption of mucosal integrity
                  during denosumab therapy including: active dental or jaw condition requiring oral
                  surgery or tooth extraction; non-healed dental or oral surgery or planned
                  invasive dental procedures during the anticipated course of study therapy

               -  Unstable systemic disease, excluding osteosarcoma, such as unstable proximal
                  renal tubule dysfunction (Fanconi syndrome) or congestive heart failure

          -  Pregnancy and breast feeding

               -  Female patients who are pregnant; a pregnancy test is required for female
                  patients of childbearing potential

               -  Lactating females who plan to breastfeed their infants while on study therapy and
                  through 5 months after completion of study therapy

               -  Sexually active patients of reproductive potential who have not agreed to use an
                  effective contraceptive method for the duration of their study participation and
                  for 5 months after the end of study treatment

          -  All patients and/or their parents or legal guardians must sign a written informed
             consent

          -  All institutional, Food and Drug Administration (FDA), and National Cancer Institute
             (NCI) requirements for human studies must be met