Inclusion Criteria:

• Locally advanced, unresectable or metastatic UPS or MFS (or Grade 1 MFS with documented metastases) confirmed by histologic analysis by the treating institution pathologist, including pleomorphic undifferentiated sarcoma, undifferentiated high-grade pleomorphic sarcoma, pleomorphic sarcoma with prominent inflammation, pleomorphic sarcoma with giant cells, malignant fibrous histiocytoma (including storiform-pleomorphic and inflammatory subtypes) and myxofibrosarcoma located deep to the fascia in muscle (MFS). “MFS” of the retroperitoneum, abdominal cavity and pelvis is not allowed. Pathology report and enrollment checklist will be reviewed by sponsor prior to randomization.
• Documented progression by radiographic criteria (e.g., RECIST, WHO, Choi) on or following chemotherapy.
• Measurable disease by RECIST 1.1.
• Age of > 12 years or older and weight > 40 kg
• Eastern Cooperative.
• Resolution of all acute AEs resulting from prior cancer therapies to National Cancer Institute Common Terminology Criteria for Adverse Events version 5.0 (NCI CTCAE v5.0) Grade -study baseline (except alopecia or neuropathy)
• Adequate organ function as defined by the following criteria: Serum aspartate transaminase (AST; serum glutamic oxaloacetic transaminase [SGOT]) and serum alanine transaminase (ALT; serum glutamic pyruvic transami 1.5 x upper limit of normal (ULN) where bilirubin < 2.5 x ULN is allowed 0 Absolute lymphocyte count (ALC) > 500/uL randomization) 9.0 g/dL (without transfusion support within 14 days prior to randomization; erythropoietin or darbepoetin permitted) 75 times the upper limit of normal or creatinine clearance > 30 mL/min by Cockcroft-Gault formula 5 unless the patient is receiving a direct Factor Xa inhibitor Serum albumin > 3.0 g/Dl 8. Willingness and ability to consent (and assent if under age 18) for self to participate in study.
• Willingness and ability to comply with scheduled visits, treatment plan, laboratory tests, and other study procedures.
• UPS/MFS FFPE tumor specimen or slides thereof (fine needle aspiration is not acceptable), unless archival tissue is unavailable and biopsy is unsafe or unfeasible.
• Men who are sterile (including vasectomy confirmed by post vasectomy semen analysis) OR agree to use a condom with spermicide and to not donate sperm during the study and for at least 180 days following last dose of envafolimab or ipilimumab (if applicable) whichever is later.
• Women of non-child bearing potential due to surgical sterilization (at least 6 weeks following surgical bilateral oophorectomy or hysterectomy) or medicallydocumented ovarian failure confirmed by medical history (i.e., no menstrual bleeding for more than 12 months in women aged 45 years or more), OR women of child bearing potential who test negative for pregnancy at time of enrollment based on serum or urine pregnancy test and agree to use at least 2 acceptable methods of birth control, one of which must be highly effective, during the study and for at least 180 days after stopping envafolimab or ipilimumab (if applicable) whichever is later.

Exclusion Criteria:

• Prior treatment with a PD-(L)1 or CTLA-4 inhibitor.
• Prior treatment with any immunomodulatory therapy, including T cell therapy.
• QTcF > 480 ms.
• Autoimmune disease requiring systemic treatment within the past twelve months.
  • Note: Vitiligo, type 1 diabetes mellitus, residual hypothyroidism due to autoimmune thyroiditis only requiring hormone replacement, and conditions, including eczema, not expected to recur in the absence of an external trigger are permitted.)
• Condition requiring systemic treatment with either corticosteroids (> 10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days prior to study treatment.
  • Note: Inhaled and topical steroids, and adrenal replacement steroid doses > 10 mg daily prednisone equivalent or steroids for the treatment of contrast allergies, are permitted in the absence of active autoimmune disease.
• History of or active interstitial lung disease
• More than two prior lines (may be combination regimen) of chemotherapy (not including hormonal treatments) for UPS/MFS (neoadjuvant/adjuvant treatment does not count as a line of treatment if completed > 12 months prior to randomization).
• Current treatment or participation on another therapeutic clinical trial.
• Women who are pregnant or breastfeeding.
• Receipt of systemic anticancer therapy, including investigational agents, within 5 -life or 14 days of starting study treatment, whichever is shorter.
• Major surgical procedure or significant traumatic injury within 4 weeks prior to randomization and must have fully recovered from any such procedure or injury:
  • planned surgery (if applicable) or the anticipated need for a major surgical procedure within the next six months.
  • Note: the following are not considered to be major procedures and are permitted up to 7 days before randomization: Thoracentesis, paracentesis, laparoscopy, thoracoscopy, tube thoracostomy, bronchoscopy, endoscopic ultrasonographic procedures, mediastinoscopy, skin biopsies, and imaging-guided biopsy for diagnostic purposes.
• Patients who have received days prior to randomization.
• Uncontrolled hypertension defined as systolic > 170 or diastolic > 100 mm Hg on the average of the 3 most recent BP readings. Anti-hypertensives may be started prior to randomization.
• Ascites or pleural effusion that required intervention within three months prior to randomization.
• Pericardial effusion (except clinically insignificant trace or small effusion identified by echocardiogram or another imaging study) within three months prior to randomization.
• History of brain involvement with cancer, spinal cord compression, or carcinomatous meningitis, or new evidence of brain or leptomeningeal disease.
• Angina, myocardial infarction, symptomatic congestive heart failure, cerebrovascular accident, transient ischemic attack, arterial embolism, symptomatic pulmonary embolism, percutaneous transluminal coronary angioplasty (PTCA) or coronary artery bypass graft (CABG) within 6 months prior to randomization.
• Active bleeding. Patients who have been uneventfully anti-coagulated with a direct Factor Xa inhibitor or low molecular weight heparin are eligible
• Hemoptysis (> ½ teaspoon [2.5 mL] of bright red blood) within 6 months prior to randomization, unless definitively treated without recurrence for > 28 days prior to randomization.
• Thrombolytic use (except to maintain i.v. catheters) within 10 days prior to randomization
• Known active viral or nonviral hepatitis or cirrhosis, except patients with Hepatitis C infection and undetectable virus following treatment are eligible.
• History of prior malignancy unless the cancer is currently in complete remission per adequately treated basal cell or squamous cell skin cancer, a history of breast cancer and no evidence of disease on hormonal therapy to prevent recurrence or prostate cancer on adjuvant hormonal therapy with undetectable PSA are eligible.
• Known human immunodeficiency virus (HIV) unless CD4+ T cell count > 350 cells/µL with an undetectable viral load.
• Active infection that requires systemic treatment.