Concurrent Immunotherapy and Systemic Therapy With Stereotactic Body Radiation Therapy (SBRT) for Stage IV Cancers (COINSSS IV)

Inclusion Criteria: * Histologically proven advanced or stage IV head \& neck, non-small cell lung cancer, cervical, esophageal, gastric, and gastroesophageal cancer at least 6 metastases that are eligible for SBRT comprising: lung, liver, adrenal glands, bone, and lymph node sites with at least 1 other lesion meeting RECIST criteria of which this additional lesion not be treated with SBRT (biopsies performed for diagnosis are standard of care). * At least 6 metastases eligible for SBRT comprising: lung, liver, adrenal glands, bone, and lymph node sites * The 1 irradiated lesion must have a max point dose of 5Gy or less. * Eligible for Immunotherapy for an FDA-approved indication as defined in section 6.1. NOTE: No limit is placed on prior systemic treatment unless it affects the eligibility for administration of immune checkpoint inhibitor therapy. * If prior treatment with chemotherapy or radiotherapy or surgery has occurred: Prior chemotherapy or radiation must have concluded \> 21 days prior to the start of study treatment. Exception: study treatment can start within 2-3 days following GKS \[gamma knife surgery\] or whole brain radiation therapy \[ WBRT\], as long as patient is not experiencing ongoing/residual AE's related to GKS or WBRT at discretion of treating physician. * First Line immunotherapy-based treatments only. The patient may have received prior cycles of immunotherapy, but has to be on the first line of immunotherapy-based treatments. * If non-small cell lung cancer patient with pembrolizumab, PD-L1 testing CPS score \> or = to 50% will have to be shown * If cervical cancer patient on secondary line therapy with pembrolizumab, CPS score of \> or = to 1 will have to be done. Please note, second line therapy with pembrolizumab is only allowed if the patient's first line of therapy did NOT include immunotherapy. * If non-small cell lung cancer on first line ipilimumab in combination with nivolumab, PD-L1 of 1% and negative epidermal growth factor receptor (EGFR) or anaplastic lymphoma kinase (ALK) genomic tumor aberrations. * If pembrolizumab is given for a gastric cancer, a PD-L1 expression (CPS =1) will need to be shown * If pembrolizumab is given as a single agent treatment after progression of one prior systemic therapy agent for esophageal or gastroesophageal squamous cell carcinoma histology, a PD-L1 (CPS=1) expression will have to be shown. * ECOG Performance Status 0 - 1 (see Appendix A). * Life expectancy \> or equal to 6 months. * Adequate organ and bone marrow function prior to study treatment as defined by: Thresholds for lab values prior to initiation of study treatment. * ANC \> or equal to 1,000/mm3 * Platelets \> or equal to 100,000/mm3 * Total bilirubin \< or equal to or equal to 1.5 x ULN * AST and ALT - With hepatic metastasis, \< or equal to or equal to 5 x ULN. If no hepatic metastasis, \< or equal to 2.5 times x ULN * Creatinine Or Creatinine Clearance \< or equal to 1.5 x ULNand/or CrCl \> or equal to 30ml/min (per 24-hour urine collection) or calculated according to the Cockcroft-Gault formula (Appendix B) * No previous or concurrent malignancy is allowed except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer for which the patient has been disease free for the past 3 years. * Non-pregnant and non-nursing women -Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment. * Women of childbearing potential and men must agree to use adequate contraception methods prescribed their the patients primary care physician, urologist, or obstetrician/gynecologist prior to study entry and for the duration of study participation. * Subjects should use adequate birth control for at least 3 months after the last administration of immune checkpoint inhibitors. * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Presence of \< or equal to 5 sites amenable to SBRT * Ineligible for immune checkpoint inhibitors based on package insert of the chosen immune checkpoint inhibitor * No more than 7 metastatic sites to an organ, defined as liver, left lung, right lung, single anatomically bone site (e.g. femur, humerus, single vertebral body). NOTE: Multiple different vertebral bodies are allowed. * Peritoneal involvement, at the discretion of the study PI. NOTE: Peritoneal metastasis does not exclude GI nor cervical cancer, except in cases where there is a separate focus of spread to the peritoneum. * Presence of liver cirrhosis of any grade prohibits SBRT to the liver. NOTE: Pt can enroll to trial if receiving SBRT to other non-liver metastatic sites. * A plan that cannot meet organ at risk tolerance (as defined in section 6.7.2.1) Auto-immune diagnosis Medications prohibited while receiving concurrent SBRT: gemcitabine, Adriamycin, VEGF or BRAF inhibitors. NOTE: However, if the patient is on the prohibited agent(s), the patient is still eligible for the trial so long as the prohibited agent can safely be held for at least 1 month before starting SBRT, during SBRT, and 1 month after completion of SBRT. -Major surgical procedure (including craniotomy and open brain biopsy) or significant traumatic injury (injury requiring immediate surgical intervention or involving loss of consciousness) within 14 days prior to registration or those patients who receive a nonCNS minor surgical procedures (e.g. core biopsy or fine needle aspiration) within 3 days prior to registration. NOTE: There is no waiting period for central line placement. There is a 7-day window for recovery prior to registration for patients who underwent stereotactic biopsy of the brain. * Active clinically serious infection \> CTCAE Grade 2. * Serious non-healing wound, ulcer or bone fracture. * Uncontrolled inter-current illness. This includes, but is not limited to: ongoing or active infection; symptomatic congestive heart failure (NYHA class III or IV); unstable angina pectoris or new onset angina that began within the last 3 months; cardiac ventricular arrhythmias requiring anti-arrhythmic therapy; thrombotic/ embolic events such as cerebrovascular accident, including transient ischemic attacks within the past 6 months; * Uncontrolled hypertension defined as systolic blood pressure \>150 mmHg or diastolic pressure \> 90 mmHg, despite optimal medical management; Known human immunodeficiency virus (HIV) infection or chronic Hepatitis B or C; Known Grade 3 or 4 neurotoxicity. * Receipt of live attenuated vaccine within 30 days prior to the first dose of ICI. Note: Patients, if randomized, should not receive live vaccine while receiving ICI and up to 30 days after the last dose of ICI. -Inclusion of Women and Minorities - Consistent with NIH policy, both men and women of all races and ethnic groups are eligible for this trial.