Inclusion Criteria:

          -  REGISTRATION TO STEP 1

          -  Patient must have histologically confirmed HER2 negative metastatic esophageal or
             gastric adenocarcinoma (American Joint Committee on Cancer [AJCC] 8th edition)

          -  Patient must have oligometastatic disease at the time of registration, which is
             defined as the following:

               -  At most 3 radiologically visible metastatic lesions (not sites), in addition to
                  the primary site. Computed tomography (CT) or magnetic resonance imaging (MRI)
                  scans will be performed for staging purposes. Patients with oligometastatic sites
                  that are only detected with positron emission tomography (PET)/CT will be
                  eligible for participation, as long as radiation planning and administration is
                  feasible after discussion with treating radiation oncologist. Malignant lymph
                  node should be at least 1 cm in size or biopsy proven involved by disease

               -  Anatomically defined lymphadenopathy will be considered as 1 site of metastatic
                  disease. For example, 2 enlarged paraaortic lymph nodes will be considered as one
                  site, and 2 additional sites will be allowed to meet protocol definition of
                  oligometastatic disease. However, if supraclavicular or cervical nodes are
                  involved for distal esophageal tumors or gastric tumors, these are counted
                  separately from intrathoracic nodes. For upper thoracic/cervical esophageal
                  tumors, the involvement of celiac nodes are counted separately from intrathoracic
                  nodes. Intrathoracic nodes, defined as hilar and mediastinal nodes, will be
                  collectively counted as one

               -  Patients with radiologically evident peritoneal metastasis will be excluded.

          -  Patient must have an Eastern Cooperative Oncology Group (ECOG) performance status 0-1

          -  Women of childbearing potential and sexually active males must not expect to conceive
             or father children by using accepted and effective method(s) of contraception (both
             double barrier contraception and birth control pills or implants) or by abstaining
             from sexual intercourse for at least one month after the last dose of protocol
             treatment and continuing for 5 months after the last dose of protocol treatment (for
             female patients) and for 7 months after the last dose of protocol treatment (for male
             patients who are sexually active with women of child bearing potential [WOCBP]).
             Investigators must counsel WOCBP and male patients who are sexually active with WOCBP
             on the importance of pregnancy prevention and the implications of an unexpected
             pregnancy

          -  Absolute neutrophil count (ANC) >= 1.5 x 10^9/L (obtained within 28 days prior to
             registration)

          -  Hemoglobin >= 8 g/dL (obtained within 28 days prior to registration)

          -  Platelets (PLT) >= 100 x 10^9/L (obtained within 28 days prior to registration)

          -  Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =< 3.0 x upper limit
             of normal (ULN) (obtained within 28 days prior to registration)

          -  Bilirubin =< 1.5 x institutional ULN (obtained within 28 days prior to registration)

          -  Serum creatinine =< 1.5 x institutional ULN (Cockcroft and Gault formula) (obtained
             within 28 days prior to registration)

          -  Albumin > 2.5 g/dL (obtained within 28 days prior to registration)

          -  Patient must be able to understand and willing to sign and date the written voluntary
             informed consent form prior to any protocol-specific procedures

          -  Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral
             therapy with undetectable viral load within 6 months are eligible for this trial.
             Patients must have CD4 > 200 at the time of registration

               -  NOTE: HIV testing is not required for eligibility

          -  Patients with a prior or concurrent malignancy whose natural history or treatment does
             not have the potential to interfere with the safety or efficacy assessment of the
             investigational regimen are eligible for this trial

          -  Patients who had prior definitive treatment for early stage EGA with either surgery or
             chemoradiation are eligible for participation as long as recurrent disease developed
             at least 6 months after completion of all prior therapies

          -  Any major surgery must have been completed >= 4 weeks prior to registration

          -  REGISTRATION TO STEP 2

          -  Patient must have histologically confirmed HER2 negative metastatic esophageal or
             gastric adenocarcinoma (AJCC 8th edition) with stable disease after about 4 months of
             fluorouracil, leucovorin calcium, and oxaliplatin (FOLFOX) or 6 cycles of capecitabine
             and oxaliplatin (CAPOX) (Step 1 treatment)

          -  Patient must have no evidence of disease progression based on Response Evaluation
             Criteria in Solid Tumors (RECIST) criteria since Step 1 registration. Patients with
             complete radiologic response are eligible for Step 2

          -  Patient must have an ECOG performance status 0-1

        Exclusion Criteria:

          -  Patient must not have any contraindications to 5-fluorouracil (5-FU) or capecitabine,
             oxaliplatin

          -  Patient must not have any contraindications to radiation therapy based on consultation
             with a radiation oncologist. Formal radiation oncology evaluation will be required for
             eligibility purposes. Prior palliative or definitive radiation to the primary site is
             allowed, as long as it was completed at least 2 weeks before registration

          -  Women must not be pregnant or breast-feeding due to the potential harm to unborn fetus
             and possible risk for adverse events in nursing infants with the treatment regimens
             being used

               -  All females of child bearing potential must have a serum or urine pregnancy test
                  to rule out pregnancy within 14 days prior to registration

               -  A female of childbearing potential is any woman, regardless of sexual orientation
                  or whether they have undergone tubal ligation, who meets the following criteria:
                  has achieved menarche at some point, has not undergone a hysterectomy or
                  bilateral oophorectomy; or has not been naturally postmenopausal (amenorrhea
                  following cancer therapy does not rule out childbearing potential) for at least
                  24 consecutive months (i.e., has had menses at any time in the preceding 24
                  consecutive months)

          -  Patient must not have had any prior treatment with 5-FU or capecitabine and/or
             oxaliplatin containing systemic therapy

               -  NOTE: Patients previously treated with radiosensitizing doses of 5-FU will be
                  eligible for participation as long as adequate time has elapsed from past
                  treatments

               -  NOTE: Patients who received systemic 5-FU or capecitabine and/or oxaliplatin as
                  part of the treatment for their locoregional disease are eligible for
                  participation, as long as all definitive therapy has been completed at least 6
                  months prior to trial enrollment

          -  Patients with known central nervous system (CNS) metastasis will be excluded from
             trial participation, regardless of the status of the CNS disease

          -  Patient must not have any uncontrolled intercurrent illness including, but not limited
             to ongoing or active infection requiring treatment, symptomatic congestive heart
             failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social
             situations that would limit compliance with study requirements

          -  Patient must not have had live vaccines within 30 days prior to registration. Examples
             of live vaccines include, but are not limited to, the following: measles, mumps,
             rubella, chicken pox, yellow fever, rabies, Bacillus Calmette Guerin (BCG), and
             typhoid (oral) vaccine. Seasonal influenza vaccines for injection are generally killed
             virus vaccines and are allowed; however, intranasal influenza vaccines (e.g.,
             Flu-Mist) are live attenuated vaccines and are not allowed