Inclusion Criteria:

          -  Patients with stage IV or locally advanced unresectable gastrointestinal
             adenocarcinomas (gastric, gastroesophageal junction [GEJ], cholangiocarcinoma,
             hepatocellular, pancreas, colorectal, small intestinal tumors) who have failed at
             least one prior therapy (dose escalation phase)

          -  Patients with pancreatic adenocarcinoma; patients must have histologic diagnosis and
             either locally advanced unresectable or metastatic disease that has failed at least
             one standard regimen; eight patients must have tumors that are accessible for biopsy
             and sign the informed consent for paired biopsy study (dose escalation phase, arm A)

          -  Patients with colorectal adenocarcinoma; patients must have histologic diagnosis and
             either locally advanced unresectable or metastatic disease and have previously
             received oxaliplatin, irinotecan, and fluoropyrimidine; eight patients must have
             tumors that are accessible for biopsy and sign the informed consent for paired biopsy
             study (dose escalation phase, arm B)

          -  Be willing and able to provide written informed consent/assent for the trial

          -  Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST)
             1.1

          -  Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG)
             performance scale

          -  Absolute neutrophil count (ANC) ≥ 1,500 cells/µL

          -  Platelets ≥ 100,000 cells/µL

          -  Hemoglobin ≥ 9 g/dL or ≥ 5.6 mmol/L without transfusion or erythropoietin (EPO)
             dependency (within 7 days of assessment)

          -  Serum creatinine ≤ 1.5 x upper limit of normal (ULN) OR measured or calculated
             creatinine clearance (glomerular filtration rate [GFR] can also be used in place of
             creatinine or creatinine clearance [CrCl]) ≥ 60 mL/min for subject with creatinine
             levels > 1.5 x institutional ULN

               -  Creatinine clearance should be calculated per institutional standard

          -  Serum total bilirubin ≤ 1.5 x ULN OR direct bilirubin ≤ ULN for subjects with total
             bilirubin levels > 1.5 ULN

          -  Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and
             alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase [SGPT]) ≤ 2.5 x
             ULN OR ≤ 5 x ULN for subjects with liver metastases

          -  Albumin ≥ 2.5 mg/dL

          -  International normalized ratio (INR) or prothrombin time (PT) ≤ 1.5 x ULN unless
             subject is receiving anticoagulant therapy as long as PT or partial thromboplastin
             time (PTT) is within therapeutic range of intended use of anticoagulants

          -  Activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN unless subject is receiving
             anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use
             of anticoagulants

          -  Female subject of childbearing potential should have a negative urine or serum
             pregnancy within 72 hours prior to receiving the first dose of study medication; if
             the urine test is positive or cannot be confirmed as negative, a serum pregnancy test
             will be required

          -  Male subjects of childbearing potential must agree to use an adequate method of
             contraception, starting with the first dose of study therapy through 120 days after
             the last dose of study therapy.

               -  Note: Abstinence is acceptable if this is the usual lifestyle and preferred
                  contraception for the subject

          -  Female subjects of childbearing potential must be willing to use an adequate method of
             contraception for the course of the study through 120 days after the last dose of
             study medication

               -  Note: Abstinence is acceptable if this is the usual lifestyle and preferred
                  contraception for the subject

        Exclusion Criteria:

          -  Is currently participating and receiving study therapy or has participated in a study
             of an investigational agent and received study therapy or used an investigational
             device within 4 weeks of the first dose of treatment

          -  Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any
             other form of immunosuppressive therapy within 7 days prior to the first dose of trial
             treatment

          -  Has a known history of active tuberculosis (TB) (Bacillus tuberculosis)

          -  Hypersensitivity to pembrolizumab or history of severe allergic or hypersensitivity
             reactions to excipients (e.g., polyethylene glycol [PEG] 300 and polysorbate 80)

          -  Clinically significant cardiovascular disease or peripheral vascular (e.g. myocardial
             infarction, unstable angina within 6 months of study entry), symptomatic congestive
             heart failure, serious uncontrolled cardiac arrhythmia requiring medications, baseline
             corrected QT (QTc) > 450 msec or previous history of QT prolongation while taking
             other medications

          -  Other medications, or severe acute/chronic medical or psychiatric condition, or
             laboratory abnormality that may increase the risk associated with study participation
             or study drug administration, or may interfere with the interpretation of study
             results, and in the judgment of the investigator would make the subject inappropriate
             for entry into this study

          -  Has had a prior anti-cancer monoclonal antibody (mAb) within 4 weeks prior to study
             day 1 or who has not recovered (i.e., ≤ grade 1 or at baseline) from adverse events
             due to agents administered more than 4 weeks earlier

          -  Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy
             within 2 weeks prior to study day 1 or who has not recovered (i.e., ≤ grade 1 or at
             baseline) from adverse events due to a previously administered agent

               -  Note: Subjects with ≤ grade 2 neuropathy are an exception to this criterion and
                  may qualify for the study

               -  Note: If subject received major surgery, they must have recovered adequately from
                  the toxicity and/or complications from the intervention prior to starting therapy

          -  Has a known additional malignancy that is progressing or requires active treatment;
             exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the
             skin that has undergone potentially curative therapy or in situ cervical cancer

          -  Has known active central nervous system (CNS) metastases and/or carcinomatous
             meningitis; subjects with previously treated brain metastases may participate provided
             they are stable (without evidence of progression by imaging for at least four weeks
             prior to the first dose of trial treatment and any neurologic symptoms have returned
             to baseline), have no evidence of new or enlarging brain metastases, and are not using
             steroids for at least 7 days prior to trial treatment; this exception does not include
             carcinomatous meningitis which is excluded regardless of clinical stability

          -  Has active autoimmune disease that has required systemic treatment in the past 2 years
             (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive
             drugs); replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid
             replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a
             form of systemic treatment

          -  Has known history of, or any evidence of active, non-infectious pneumonitis

          -  Has an active infection requiring systemic therapy

          -  Has known substance abuse disorders that would interfere with cooperation with the
             requirements of the trial

          -  Is pregnant or breastfeeding, or expecting to conceive or father children within the
             projected duration of the trial, starting with the pre-screening or screening visit
             through 120 days after the last dose of trial treatment

          -  Has received prior therapy with an anti-programmed death (PD)-1, anti-PD-L1, or
             anti-PD-L2 agent

          -  Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)

          -  Has known active hepatitis B (e.g., hepatitis surface antigen [HBsAg] reactive) or
             hepatitis C (e.g., hepatitis C virus [HCV] ribonucleic acid [RNA] [qualitative] is
             detected)

          -  Has received a live vaccine within 30 days of planned start of study therapy

               -  Note: Seasonal influenza vaccines for injection are generally inactivated flu
                  vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist)
                  are live attenuated vaccines, and are not allowed