A Vaccine (Ad5.F35-hGCC-PADRE) for the Treatment of Gastrointestinal Adenocarcinoma

Inclusion Criteria: * Have Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Subjects with tumors specified below, who are at high risk of relapse, have been treated with curative intent, and have no evidence of disease (NED) following front-line therapy with surgery, radiation therapy, and/or chemotherapy. NED includes, where applicable, surgical (macroscopic tumor margin, at the time of surgery), and radiological evidence of disease. Residual lesions identified by microscopic/frozen margins and biochemical markers are permitted. Therapy must have been completed no fewer than four weeks, and no later than 25 weeks, before the first dose of Ad5.F35-hGCC-PADRE * For tumor-specific criteria, please refer to the information below: \* Pancreatic ductal adenocarcinoma \*\* Stage I, II, III * Neuroendocrine tumors of the pancreas are not permitted \* Colorectal adenocarcinoma * Stage III; stage IV following metastasectomy \* Gastric adenocarcinoma * Stage IIA, IIB, III * Gastrointestinal stromal tumors of the stomach are not permitted \* Esophageal adenocarcinoma \*\* Stage IIB, III * Esophageal squamous cell carcinomas are not permitted * Have an anticipated life expectancy of greater than 12 weeks * Absolute neutrophil count (ANC) \>= 1000 cells/mL * Platelets \>= 75,000 /mL * Hemoglobin \>= 9.0 g/dL * Serum creatinine \< 2.0 mg/dL * For other blood and urine tests including blood chemistry, hepatic and renal functions, test results should not be worse than grade 1 levels of abnormalities defined by Common Terminology Criteria for Adverse Events (CTCAE), National Cancer Institute (NCI) version 5 issued by the United States (US) Department of Health and Human Services * For women and men of childbearing potential, a medically acceptable method of highly effective contraception (oral hormonal contraceptive, condom plus spermicide, or hormonal implants) or abstinence must be used throughout the study period and for 28 days after their final vaccine administration (a barrier method of contraception must be employed by all subjects \[male and female\], regardless of other methods unless abstinent). A negative serum or urine pregnancy test is required as part of screening. Women of childbearing potential is defined as any female who has experienced menarche and who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy) or who is not postmenopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. In addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/ml * Be willing to comply with all the study procedures * All subjects must be able to comprehend and sign a written informed consent document Exclusion Criteria: * Have a known history or evidence of residual disease after definitive surgery * Have a known metastasis in the brain or central nervous system * Prior receipt of immunotherapy or experimental medications after completion of standard adjuvant therapy * Have a history of splenectomy * Have a history of distal pancreatectomy * Concurrent use of systemic steroids or immunosuppressive drugs (use of topical or inhaled steroids will be allowed) * Have any immunodeficiency disease or immunocompromised state (e.g., use of immunosuppressive agents, chemotherapy or radiation therapy within four weeks of study treatment) * Have active autoimmune disease or history of autoimmune disease or a transplant recipient requiring systemic steroids or other immunosuppressive treatment * Have received a diagnosis of human immunodeficiency virus (HIV), hepatitis B, or hepatitis C (subjects who are hepatitis C positive may be enrolled if they are confirmed with negative viral load at screening) * Other malignancy within last 5 years except curatively treated non-melanomatous skin cancer and curatively treated carcinoma in situ of the uterine cervix, or early-stage (stage A or B1) prostate cancer * Have a history of inflammatory bowel disease * Have a history of serious reaction to adenovirus * Have an intercurrent illness that is either life-threatening or of clinical importance such that it might limit study compliance (such illnesses include, but are not limited to, ongoing or active infection, metabolic or neurologic disease, peripheral vascular disease, or psychiatric illness) * Have insufficient peripheral venous access to permit completion of the study phlebotomy regimen * Consumes greater than three glasses of alcoholic beverages (1 glass is approximately equivalent to: beer \[354 mL/12 ounces\], wine \[118 mL/4 ounces\], or distilled spirits \[29.5 mL/1 ounce\]) per day and cannot refrain from alcohol for the duration of the trial * Has a history of use of illicit drugs (e.g., opioids, cocaine, amphetamines, hallucinogens, etc.) that could potentially interfere with adherence to study procedures or requirements * Be a woman who is pregnant or breastfeeding * Have an unhealed surgical wound * Have had major surgery or significant traumatic injury occurring within 28 days before treatment or anticipated surgery or procedure requiring general anesthesia during the study participation (including four weeks after last dose of vaccine)