The tumor must be unilateral invasive adenocarcinoma of the breast on histologic examination Histologic documentation of invasive adenocarcinoma of the breast There must be histologic confirmation of a diagnosis of colorectal adenocarcinoma. Males diagnosed with histologically confirmed, adenocarcinoma of the prostate based on core biopsy prior to study entry from transrectal ultrasonography (TRUS) Patients with cytologic evidence of adenocarcinoma in situ Histologic confirmation of adenocarcinoma of the prostate Histologic confirmation of prostate adenocarcinoma diagnosis Evidence of neuroendocrine tumor, duodenal adenocarcinoma, or ampullary adenocarcinoma Histological proof of adenocarcinoma of the prostate Diagnosis of pancreatic islet neoplasm, acinar cell carcinoma, non- adenocarcinoma (i.e., lymphoma, sarcoma), adenocarcinoma originating from the biliary tree, or cystadenocarcinoma Must have histologic or cytologic confirmation of recurrent metastatic pancreatic adenocarcinoma based on standard diagnostic criteria. Recurrence must be documented by diagnostic biopsy. Does not have a diagnosis of prostate adenocarcinoma Histologic confirmation of diagnosis of adenocarcinoma of the prostate will be required by biopsy Documented pathologic confirmation of prostate adenocarcinoma Patients must have histologic or cytologic confirmation of the diagnosis of invasive adenocarcinoma of the breast. Patients with a histologic diagnosis of adenocarcinoma of the esophagus located distal to the carina Histologically proven adenocarcinoma of the prostate obtained within 6 months of screening; patients in whom a diagnosis of high-risk localized or locally-advanced prostatic adenocarcinoma is suspected based on a serum PSA > 20 ng/mL or clinical T3 disease by digital rectal examination, but who have not yet undergone diagnostic prostate biopsy, will be eligible for screening and initial MRI and targeted prostate cancer biopsies which will be obtained at the same time as diagnostic biopsies; those patients in whom the diagnostic biopsies confirm prostatic adenocarcinoma will be permitted to continue with study treatment if they meet all additional eligibility criteria Have histologically proven adenocarcinoma of the colon or rectum Patients with adenocarcinoma of the prostate that in the opinion of the urologist could be resected after response to systemic therapy; ductal adenocarcinoma is permitted Patients with cytologic evidence of adenocarcinoma in situ No histologic documentation of breast adenocarcinoma Must have operable gastric adenocarcinoma, T2-T4a, N0-N3, M0 Histologic confirmation of invasive adenocarcinoma originating in the breast Histological or cytologic evidence of adenocarcinoma of the prostate confirmed at local institution Diagnosis of adenocarcinoma of the prostate, confirmed by H. Lee (L.) Moffitt Cancer Center review HER2 expressing adenocarcinoma of the esophagus centrally Histologically documented adenocarcinoma (including the histologic variants of adenocarcinoma) of the colon or rectum adenocarcinoma of the prostate that has been surgically treated with a post-treatment PSA that is undetectable; Part B: Esophagogastric Adenocarcinoma: Prior history of invasive adenocarcinoma of colon or rectum. Patients with adenocarcinoma of unknown primary are excluded Appendiceal adenocarcinoma basket\r\n* Metastatic appendiceal adenocarcinoma\r\n* Not considered candidate for curative surgery Histologic confirmation of adenocarcinoma of the prostate by biopsy; Patients with a histologic diagnosis of adenocarcinoma of the prostate Participants with adenocarcinoma of the esophagus are excluded. Evidence or history of metastatic adenocarcinoma of the prostate Pathologically confirmed adenocarcinoma of the lung. Grade 3 adenocarcinoma Histologically documented diagnosis of adenocarcinoma of the prostate (PCa) with no histologic variants Histologic proof of prostate adenocarcinoma Histologic variants in the primary tumor (histologic variants other than adenocarcinoma) Histologic diagnosis of adenocarcinoma of the prostate Histologic or cytologic diagnosis of pancreas adenocarcinoma advanced or recurrent (stage III or IV) that is unresectable; histologic or cytologic pathology from any prior surgery is sufficient for diagnosis Patients with a histologic diagnosis of adenocarcinoma of the upper gastrointestinal tract and hepatobiliary system, including patients with any of the following diagnoses and settings who are candidates to receive radiation with concurrent continuous infusion 5-FU or oral capecitabine chemotherapy:\r\n * Pancreatic adenocarcinoma (unresected or adjuvant)\r\n * Duodenal adenocarcinoma (unresected or adjuvant)\r\n * Extra-hepatic cholangiocarcinoma (unresected or adjuvant)\r\n * Gastric adenocarcinoma (unresected or adjuvant)\r\n * Gastroesophageal junction adenocarcinoma (adjuvant) Patients with a histologic diagnosis of adenocarcinoma of the prostate Patients with verrucous or adenocarcinoma Diagnosis of pancreatic islet neoplasm, acinar cell carcinoma, non-adenocarcinoma (eg, lymphoma, sarcoma), adenocarcinoma originating from the biliary tree or cystadenocarcinoma Histologic variants other than adenocarcinoma in the primary tumor Diagnosis of pancreatic islet neoplasm, acinar cell carcinoma, non-adenocarcinoma, adenocarcinoma originating from the biliary tree or cystadenocarcinoma Have a history of a primary adenocarcinoma of the colon and / or rectum Prior to randomization, have histological confirmation that CRC lesions were adenocarcinoma (subtypes of adenocarcinoma, e.g. mucinous adenocarcinoma are allowed). Subjects with CRC lesions of other histological types, including mixed type with predominant adenocarcinoma, will not be eligible to be randomized to study treatment. The subject has a proven histologic diagnosis of prostate adenocarcinoma, but may have undergone prior surgery and/or radiation LUNG ADENOCARCINOMA COHORT (COHORT 3 ONLY): Subjects must have histologically confirmed advanced (stage IIIB/IV) lung adenocarcinoma; the diagnosis will be confirmed by the Laboratory of Pathology/CCR/NCI Adenocarcinoma of the breast. Histologic proof of adenocarcinoma of the prostate with clinical evidence of metastatic disease to the bone Histologically-documented prostatic adenocarcinoma in >= 2 cores Histologic diagnosis of prostate adenocarcinoma plus > 50% immunohistochemical staining for neuroendocrine markers (chromogranin, synaptophysin or neuron specific enolase) Histologic confirmation of adenocarcinoma of the prostate Histologic documentation of adenocarcinoma of the prostate NON-RANDOMIZED OBSERVATIONAL COMPONENT ELIGIBILITY:\r\nHistologically-documented localized (stage < T3) prostate adenocarcinoma Histologic confirmation of adenocarcinoma of the prostate Carry a diagnosis of metastatic colon, rectum, or small bowel adenocarcinoma Patients with evidence of concurrent adenocarcinoma-in-situ The subject has a diagnosis of adenocarcinoma of the prostate Patients with a histologic diagnosis of adenocarcinoma of the esophagus located distal to the carina Diagnosis of adenocarcinoma of the prostate, confirmed by transrectal ultrasound (TRUS) biopsy Diagnosis of prostate adenocarcinoma by transrectal ultrasound (TRUS)-guided biopsy between 28 to 90 days prior to enrollment Patients must have histologically or cytologically confirmed pancreatic ductal adenocarcinoma (PDAC); pathologic confirmation is mandated before initiation of any protocol specified imaging studies or drug administrations; it is recognized that for some patients, histologic or cytologic confirmation of cancer may be obtained following study enrollment; patient volunteers to the DW- and DCE-MRI sequence parameter optimization imaging portion of the study are eligible if they have any pancreatic lesion, histologic or cytologic confirmation of pathology is not required for this patient volunteer group Any non-adenocarcinoma histologic component Biliary tract adenocarcinoma. adenocarcinoma of the colon or rectum