Inclusion Criteria:

          -  Phase I only: Histologic confirmation of pancreatic, colorectal, gastroesophageal or
             biliary adenocarcinoma, as follows:

               -  Patients with metastatic disease from pancreatic cancer who received no more than
                  2 lines of prior therapy in the metastatic setting

               -  Patients with metastatic disease from colorectal cancer who received no more than
                  3 lines of prior therapy in the metastatic setting

               -  Patients with metastatic disease from gastroesophageal cancer who received no
                  more than 1 line of prior therapy in the metastatic setting

               -  Patients with metastatic disease from biliary tract cancer who received no more
                  than 1 line of prior therapy in the metastatic setting

               -  NOTE: No prior exposure to irinotecan in the metastatic setting will be allowed
                  except in the phase I dose escalation portion and in colon cancer patients only;
                  in pancreas cancer, exposure to irinotecan is only allowed in the neoadjuvant
                  setting and no progressive disease < 3 months from last dose of irinotecan

          -  Phase Ib only: Patients with metastatic adenocarcinoma of the pancreas both unselected
             and selected for BRCA1 or BRCA2 or PALB2 mutation who have who received no more than 1
             line of prior therapy in the metastatic setting

               -  NOTE: Exposure to irinotecan is only allowed in the neoadjuvant setting and no
                  progressive disease < 3 months from last dose of irinotecan

          -  Phase II only: Patients with metastatic adenocarcinoma of the pancreas with genomic
             markers (signature) of homologous recombination deficiency (HRD) or BRCA1 or BRCA2 or
             PALB2 mutation, or HRD (non-BRCA, non-PALB) who have not received any systemic therapy
             in the metastatic setting

               -  NOTE: Exposure to irinotecan is only allowed in the neoadjuvant setting and no
                  progressive disease < 3 months from last dose of irinotecan

          -  Metastatic colorectal, pancreatic, gastroesophageal or biliary tract adenocarcinoma
             not amenable to curative resection

          -  Measurable disease

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1

          -  Absolute neutrophil count (ANC) >= 1500/mm^3 (obtained =< 21 days prior to
             registration)

          -  Platelet count >= 100,000/mm^3 (obtained =< 21 days prior to registration)

          -  Hemoglobin > 9.0 g/dL (obtained =< 21 days prior to registration)

          -  Total bilirubin =< institutional upper limit of normal (ULN) (obtained =< 21 days
             prior to registration)

          -  Aspartate transaminase (AST) =< 3 x ULN, =< 5.0 x ULN for patients with metastatic
             disease to the liver (obtained =< 21 days prior to registration)

          -  Aminotransferase (ALT) =< 3.0 x ULN, =< 5.0 x ULN for patients with metastatic disease
             to the liver (obtained =< 21 days prior to registration)

          -  Creatinine =< 1.0 mg/dL or creatinine clearance >= 45 ml/min using the Cockcroft-Gault
             formula (obtained =< 21 days prior to registration)

          -  Negative serum or urine pregnancy test done =< 7 days prior to registration and
             repeated prior to dosing on day 1 of each cycle, for individuals of childbearing
             potential only; NOTE: Individuals are considered to be of childbearing potential
             unless one of the following applies:

               -  Is postmenopausal, defined as no menses for at least 12 months without an
                  alternative medical cause; a high follicle-stimulating hormone (FSH) level
                  consistently in the postmenopausal range (30 mIU/mL or higher) may be used to
                  confirm a postmenopausal state in women not using hormonal contraception or
                  hormonal replacement therapy; however, in the absence of 12 months of amenorrhea,
                  a single FSH measurement is insufficient to confirm a postmenopausal state: or

               -  Considered to be permanently sterile; permanent sterilization includes
                  hysterectomy, bilateral salpingectomy, and/or bilateral oophorectomy

          -  Provide informed written consent

          -  Willing to return to enrolling institution for follow-up (during the Active Monitoring
             Phase of the study)

               -  Note: During the active monitoring phase of a study (i.e., active treatment and
                  observation), participants must be willing to return to the consenting
                  institution for follow-up

          -  Willing to provide tissue and blood samples for mandatory correlative research
             purposes

          -  Individuals of reproductive potential and their partners willing to practice total
             abstinence or use a highly effective method of contraception (failure rate < 1% per
             year) during treatment and for 6 months following the last dose of rucaparib; the
             following are allowable only:

               -  Ongoing use of progesterone-only injectable or implantable contraceptives (eg,
                  Depo Provera, Implanon, Nexplanon)

               -  Placement of an intrauterine device or intrauterine system

               -  Bilateral tubal occlusion

               -  Sterilization, with appropriate post-vasectomy documentation of absence of sperm
                  in ejaculate

               -  True, complete (as opposed to periodic) abstinence

        Exclusion Criteria:

          -  Any of the following because this study involves an investigational agent whose
             genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are
             unknown:

               -  Pregnant individuals

               -  Nursing individuals

               -  Persons of childbearing potential who are unwilling to employ adequate
                  contraception

          -  Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment
             of the investigator, would make the patient inappropriate for entry into this study or
             interfere significantly with the proper assessment of safety and toxicity of the
             prescribed regimens

          -  Immunocompromised patients and patients known to be human immunodeficiency virus (HIV)
             positive and currently receiving antiretroviral therapy

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

          -  Receiving any other investigational agent which would be considered as a treatment for
             the primary neoplasm

          -  Previous or concurrent cancer that is distinct in primary site or histology from
             cancer of primary site =< 3 years prior to randomization EXCEPT for curatively treated
             cervical cancer in situ, melanoma in situ, non-melanoma skin cancer and superficial
             bladder tumors [Ta (non-invasive tumor), Tis (carcinoma in situ) and T1 (tumor invades
             lamina propria)]; Note: All cancer treatments for those distinct in a primary site
             other than cancer of origin must be completed >= 3 years prior to randomization

          -  Received any prior poly ADP-ribose polymerase inhibitor (PARPi) treatment

          -  Corrected QT interval (QTc) prolongation > 480 msec, as calculated by either the
             Bazett or Fridericia formula, as per institutional standard