Inclusion Criteria:

          -  Diagnosed with biopsy-proven soft-tissue sarcoma with confirmatory pathology review at
             University of Rochester Medical Center (URMC)

          -  18 years or older.

          -  Able to provide informed consent.

          -  Resectable disease per surgical evaluation.

          -  Neoadjuvant/preoperative radiotherapy has been recommended

          -  Intermediate to high grade sarcoma on biopsy, tumor > 5 cm in size by imaging

          -  Willing to have blood draws for flow cytometry and Serametrix analysis.

          -  Willing to receive neoadjuvant radiation therapy and subsequent surgical resection.

          -  Patients with known human immunodeficiency virus (HIV) are eligible if the lymphocytes
             > 350 CD4+ cells and no detectable viral load.

          -  Women of childbearing potential (defined as any woman, who 1) has not undergone tubal
             ligation, a hysterectomy or bilateral oophorectomy; or 2) has not been naturally
             postmenopausal for at least 24 consecutive months or has had menses at any time in the
             preceding 24 consecutive months):

               -  Must not be pregnant or nursing

               -  Must have a negative pregnancy test done within 7 days prior to registration as
                  well as within 72 hrs. prior to receiving first dose of study medication

               -  Women of childbearing potential must use at least two other accepted and
                  highly-effective methods of contraception and/or agree to abstain from sexual
                  intercourse for at least 5 months after the last dose of nivolumab and/or
                  ipilimumab.

               -  Should a woman become pregnant or suspect she is pregnant while she is
                  participating in this study, she should inform her treating physician
                  immediately.

          -  Sexually active males must use at least two other accepted and highly-effective
             methods of contraception and/or agree to abstain from sexual intercourse for at least
             7 months after the last dose of nivolumab and/or ipilimumab

          -  Eastern Cooperative Oncology Group (ECOG) performance status 0 - 2

        Exclusion Criteria:

          -  Gastrointestinal stromal tumor, dermatofibrosarcoma protuberans, rhabdomyosarcoma,
             Ewing's sarcoma, low-grade sarcomas, osteosarcoma subtypes

          -  History of radiation to the affected area

          -  Evidence of metastatic disease prior to treatment

          -  Any history of prior therapy with ipilimumab or nivolumab, or any agent targeting
             PD-1, PD-L1 or CTLA-4.

          -  History of any the following:

               -  Active known or suspected autoimmune disease

               -  Active autoimmune colitis

               -  Autoimmune pan hypopituitarism

               -  Autoimmune adrenal insufficiency

               -  Known active hepatitis B or C

               -  Known active pulmonary disease with hypoxia defined as:

          -  Oxygen saturation < 85% on room air or

          -  Oxygen saturation < 88% despite supplemental oxygen

          -  No systemic treatment with either corticosteroids (> 10 mg daily prednisone
             equivalents) or other immunosuppressive medications within 14 days of registration.

          -  Second active malignancy, not including localized basal cell skin cancer, squamous
             cell skin cancer, in situ cervical cancer, ductal or lobular carcinoma in situ of the
             breast; patients with a history of other malignancies are eligible if they have been
             continuously disease-free for > 3 years prior to the time of registration.

          -  Absolute neutrophil count (ANC) <= 1,500/mm^3

          -  Platelet count <= 100,000/mm^3

          -  AST (Aspartate Aminotransferase) or ALT (Alanine Aminotransferase) => 2 x upper limit
             of normal (ULN)

          -  Thyroid stimulating hormone (TSH) outside of normal limits; supplementation is
             acceptable to achieve a TSH within normal limits; in patients with abnormal TSH if
             free T4 is normal and patient is clinically euthyroid, patient is eligible.

          -  Life expectancy under 5 years.