Immunotherapies in Combination With Stereotactic Body Radiation Radiotherapy in Microsatellite Stable (MSS) Metastatic Colorectal Cancer (mCRC)

* INCLUSION CRITERIA:
* Histologically or cytologically confirmed colorectal cancer (CRC) by the NCI Laboratory of Pathology (LP). Note: Participants must provide tumor sample or be willing to undergo biopsy to confirm the diagnosis.
* Evidence of metastatic involvement.
* History of microsatellite stable (MSS) status.
* Age \>= 18 years.
* Weight \> 35 kg.
* ECOG performance status \<= 1
* Must have measurable disease, per RECIST 1.1
* At least 2 lesions present, one of which must be amenable to SBRT and second lesion outside the radiation field must serve as target lesion to evaluate measurable disease.
* Must have progression of disease, been treated or intolerant to at least 2 lines of systemic standard of care treatment in the metastatic setting (e.g., fluoropyrimidine-, oxaliplatin-, or irinotecan-based therapy \[unless ineligible for any of these drugs\]).
* Participants with a history of RAS wild-type tumor must have progressed, been intolerant of OR refused anti-EGFR based treatment.
* Participants must have adequate organ and marrow function as defined below:

  * Leukocytes \>= 3,000/microL
  * Absolute neutrophil count \>= 1,500/microL
  * Lymphocyte count \> 500/microL
  * Platelets \>= 100,000/microL without transfusion or at least \> 48 hours post-completion of blood transfusion
  * Hemoglobin \>= 9 g/dL without transfusion or at least \> 48 hours post-completion of blood transfusion
  * International normalized ratio \<=1.5 x institutional upper limit of normal
  * (INR) and partial thromboplastin time (aPTT) (ULN) (if not receiving therapeutic anticoagulation)
  * Serum albumin \> 2.5 g/dL
  * Total bilirubin \<= 1.5 x ULN
  * Aspartate aminotransferase (AST) \<= 2.5 x institutional ULN
  * Alanine transaminase (ALT) \<= 2.5 x institutional ULN
  * Alkaline phosphatase (ALP) \<= 2.5 x institutional ULN
  * Creatinine clearance calculated by Chronic Kidney Disease Epidemiology Collaboration (CKDEPI) equation \>= 50 mL/min/1.73 m\^2 for participants with creatinine levels \>= 1.5 mg/dL
* Participants receiving therapeutic anticoagulation must be on an established, stable anticoagulation regimen prior to starting the study therapy.
* Negative human immunodeficiency virus (HIV) serological testing at screening.
* Participants seropositive for hepatitis B virus (HBV) antibody test are eligible if at screening:

  * have a negative HBV DNA test and
  * not on treatment with anti-viral therapy for HBV.
* Participants seropositive for hepatitis C virus (HCV) antibody test, are eligible if have a negative HCV RNA test at screening.
* Participants seropositive for Epstein-Barr virus (EBV) viral capsid antigen immunoglobulin M (IgM) test are eligible if have a negative EBV polymerase chain reaction (PCR) test at screening.
* Participants must have recovered from prior toxicity or adverse events to grade \<= 2 per Common Terminology Criteria for Adverse Events (CTCAE) v.5.0.
* Women of child-bearing potential (WOCBP) must agree to use a highly effective method of contraception (hormonal, intrauterine device \[IUD\], surgical sterilization, abstinence) at the study entry and up to 5 months after the last dose of the study drugs (restriction period).

Note: A woman is considered to be of child-bearing potential if she is postmenarchal, has not reached a postmenopausal state (\>= 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (i.e., removal of ovaries, fallopian tubes, and/or uterus).

* Breastfeeding participants must be willing to discontinue breastfeeding from study treatment initiation through 5 months after the last dose of the study drugs.
* Participants must be willing to co-enroll in protocol 11-C-0112, Acquisition of Blood and Tumor Tissue Samples from Patients with Gastrointestinal Cancer .
* Participants must understand and be willing to sign a written informed consent document.

EXCLUSION CRITERIA:

* Disease amenable to curative resection.
* Chemotherapy, radiation therapy, or biologic therapy within 3 weeks (or \>= 5 half-lives, whichever is shorter) prior to starting the study therapy.
* Treatment with an investigational therapy within 42 days prior to starting the study therapy.
* Treatment with systemic immunostimulatory agents (including, but not limited to, interferon and IL-2) within 4 weeks or 5 drug-elimination half-lives (whichever is longer) prior to starting the study therapy.
* History of prior treatment with TIGIT-directed treatment agents or other types of immunotherapies (e.g., prior treatment with CD137 agonists or investigational immune checkpoint blockade therapies, including anti-TIGIT, anti-PD1/anti-PDL1, anti-CTLA-4, anti-LAG3).
* Treatment with systemic immunosuppressive medication (including, but not limited to, corticosteroids, cyclophosphamide, azathioprine, methotrexate, thalidomide, and antitumor necrosis factor-alpha \[TNF-alpha\] agents) within 2 weeks prior to starting the study therapy, or anticipation of a need for systemic immunosuppressive medication during study therapy, with the following exceptions:

  --acute, low-dose systemic immunosuppressant medication (\< 10 mg of prednisone daily) or a one-time pulse dose of systemic immunosuppressant medication (e.g., 48 hours of corticosteroids for a contrast allergy).
* Treatment with therapeutic oral or IV antibiotics within 2 weeks prior to starting the study therapy.
* Treatment with a live, attenuated vaccine within 4 weeks prior to starting the study therapy.
* Major surgery within 4 weeks prior to starting the study therapy.
* Prior allogeneic stem cell or solid organ transplantation.
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to tiragolumab and atezolizumab or other agents used in a study or known hypersensitivity to Chinese hamster ovary cell products.
* History of severe allergic anaphylactic reactions to chimeric or humanized antibodies or fusion proteins.
* History of central nervous system (CNS) metastasis or leptomeningeal disease.
* Current uncontrolled tumor-related pain. Participants requiring pain medication must be on a stable regimen at study entry.
* Current or history of chronic autoimmune disease or immune deficiency (e.g., Addison s disease, multiple sclerosis, Graves disease, Hashimoto s thyroiditis, rheumatoid arthritis, hypophysitis, systemic lupus erythematosus, Wegener s granulomatosis, sarcoidosis syndrome, etc.) or other connective tissue diseases except:

  * Participants with a history of autoimmune-related hypothyroidism who are on thyroid-replacement hormone;
  * Participants with controlled Type 1 diabetes mellitus who are on an insulin regimen.
  * Participants with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., participants with psoriatic arthritis are excluded) are eligible for the study provided all following conditions are met:

    * Rash must cover \< 10% of body surface area
    * The disease is well controlled at screening and requires only low-potency topical corticosteroids
    * There has been no occurrence of acute exacerbations of the underlying condition requiring psoralen plus ultraviolet, radiation, methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high potency or oral corticosteroids within 12 months prior to starting the study therapy.
* Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently).
* Uncontrolled or symptomatic hypercalcemia (ionized calcium \> 1.5 mmol/L, calcium \> 12 mg/dL or corrected serum calcium \> ULN).
* History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest computed tomography (CT) scan.
* Severe infection within 4 weeks prior to starting the study therapy. This includes but is not limited to, hospitalizations for complications of infection, bacteremia, severe pneumonia, or any active infection that could impact participant safety.
* Active tuberculosis.
* History of significant cardiovascular disease (such as New York Heart Association Class II or greater cardiac disease, myocardial infarction, or cerebrovascular accident) within 3 months prior to starting the study therapy, unstable arrhythmia, or unstable angina within 1 year prior to starting the study therapy.
* Prior invasive malignancy, (with the exception of non-melanomatous skin cancer) unless disease-free per standard of care for a minimum of 3 years prior to starting the study therapy.
* Women of childbearing potential must have a negative serum pregnancy test result at screening.
* Any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding that contraindicates the use of investigational drugs, may affect the interpretation of the results or may render the participants at high risk of treatment complications.