• Adult subjects (Age ≥18 years) with treatment-naïve de novo or locally recurrent soft tissue sarcomas of the extremity or superficial trunk

• Histological diagnosis of grade 2 or grade 3 undifferentiated pleomorphic sarcoma (UPS), myxofibrosarcoma (MFS), de-differentiated/pleomorphic liposarcoma (DDLPS), unclassified sarcoma, and leiomyosarcoma. Pathologic terms for the unclassified sarcoma histology may include pleomorphic undifferentiated sarcoma, unclassified spindle cell sarcoma, spindle cell sarcoma not otherwise specified, pleomorphic spindle cell sarcoma, or pleomorphic fibroblastic sarcoma.

• Patient must have recent imaging (CT or MRI, as appropriate) within 8 weeks of trial enrollment demonstrating measurable disease, defined as at least one lesion that can be ccurately measured in at least one dimension (longest diameter to be recorded) as \>5 cm.

• Patients must have disease determined to be surgically resectable and candidates for upfront surgery as agreed upon by a multidisciplinary consensus (Surgical Oncology, Medical Oncology, Radiation Oncology) after presentation at sarcoma multidisciplinary conference. Resectable tumors are defined as having no significant vascular, neural, or bony involvement. Only cases where a complete surgical resection can safely be achieved are defined as resectable.

• Patients must have life expectancy \> 6 months.

• ECOG performance status ≤2 (Karnofsky ≥60%)

• For patients receiving therapeutic anticoagulation: stable anticoagulant regimen

• Patients must have adequate organ and marrow function as defined below:

∙ absolute neutrophil count ≥1,000/mcL platelets ≥100,000/mcL total bilirubin ≤ institutional upper limit of normal (ULN) AST(SGOT)/ALT(SGPT) ≤3 × institutional ULN creatinine ≤ eGFR ≥40 ml/min

• Negative HIV test at screening, with the following exception: patients with a positive HIV test at screening are eligible provided they are stable on anti-retroviral therapy, have a CD4 count ≥ 200/L, and have an undetectable viral load

• Negative hepatitis B surface antigen (HBsAg) test at screening (if relevant)

• Negative hepatitis C virus (HCV) antibody test at screening, or positive HCV antibody test followed by a negative HCV RNA test at screening (if relevant)

• a. The HCV RNA test must be performed for patients who have a positive HCV antibody test.

• Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better.

• The effects of Atezolizumab on the developing human fetus are unknown. For this reason and because doxorubicin as used in this trial is known to be teratogenic, women of childbearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy #

∙ CLN1114). This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following:

• Postmenopausal (no menses in greater than or equal to 12 consecutive months).

• History of hysterectomy or bilateral salpingo-oophorectomy.

• Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range)

• History of bilateral tubal ligation or another surgical sterilization procedure.

‣ For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods, and agreement to refrain from donating eggs, as defined below:

⁃ Women must remain abstinent or use contraceptive methods with a failure rate of 1% per year during the treatment period and for 5 months after the final dose of atezolizumab after the final dose of doxorubicin. Women must refrain from donating eggs during this same period.

⁃ A woman is considered to be of childbearing potential if she is post-menarchal, has not reached a postmenopausal state (≥ 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries, fallopian tubes and/or uterus) or another cause as determined by the investigator (e.g., Müllerian agenesis). Per this definition, a woman with a tubal ligation is considered to be of childbearing potential. The definition of childbearing potential may be adapted for alignment with local guidelines or requirements.

‣ a. Examples of contraceptive methods with a failure rate of 1% per year include: i. bilateral tubal ligation ii. male sterilization iii. hormonal contraceptives that inhibit ovulation iv. hormone-releasing intrauterine devices v. copper intrauterine devices.

⁃ The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or post ovulation methods) and withdrawal are not adequate methods of contraception. If required per local guidelines or regulations, locally recognized adequate methods of contraception and information about the reliability of abstinence will be described in the local Informed Consent Form.

⁃ Ability to understand and the willingness to sign a written informed consent document.