Inclusion Criteria:

          -  Histopathologic documentation of pancreatic adenocarcinoma, colorectal adenocarcinoma,
             cholangiocarcinoma, esophageal cancer and gastric cancer with radiographic evidence of
             metastatic disease

          -  Eastern Cooperative Oncology Group (ECOG)/Zubrod performance status of 0 or 1

          -  Women of childbearing potential (WOCBP) must be using an adequate method of
             contraception to avoid pregnancy throughout the study in such a manner that the risk
             of pregnancy is minimized; suggested precautions should be used to minimize the risk
             or pregnancy for at least 1 month before start of therapy, and while women are on
             study for at least 8 weeks after pembrolizumab is stopped; WOCBP include any female
             who has experienced menarche and who has not undergone successful surgical
             sterilization (hysterectomy, bilateral tubal ligation or bilateral oophorectomy) or is
             not postmenopausal; acceptable forms of birth control include condom, diaphragm,
             hormonal, intrauterine device (IUD), or sponge plus spermicide; abstinence is also an
             acceptable form of birth control

          -  Men must be willing and able to use an acceptable method of birth control, during and
             for at least 3 months after completion of the study, if their sexual partners are
             WOCBP

          -  Willing and able to give informed consent

          -  Adequate vein access: consider peripherally inserted central catheter (PICC) or other
             central line

          -  Patients must have adequate tissue (fresh or frozen) available or planned removal of
             adequate tissue for analysis; at least 250 mg of tumor are needed for peptide elution;
             there is no specific time limit on how long the tissue can remain frozen prior to use

          -  Patients can have any lines (including zero) of prior therapy to sign consent prior to
             tissue harvest

          -  Toxicity related to prior therapy must either have returned to =< grade 1, baseline,
             or been deemed irreversible

          -  ELIGIBILITY FOR TREATMENT: ECOG/Zubrod performance status of 0 to 2

          -  Bi-dimensionally measurable disease by radiographic imaging (computed tomography [CT]
             scan) that represents at least one measurable lesion per Response Evaluation Criteria
             in Solid Tumors (RECIST) version (v)1.1

          -  At least 4 weeks must have elapsed since the last chemotherapy, radiotherapy or major
             surgery

          -  Toxicity related to prior therapy must either have returned to less than or equal to
             grade 1, baseline, or been deemed irreversible

          -  Subjects must have received at least one line of chemotherapy prior to receiving
             adoptive T cell therapy and should have exhausted standard of care systemic therapy
             options; the decision to implement the T cell therapy will be at the discretion of the
             treating physician; the timing and total exposure to chemotherapy will depend on the
             tumor type in question (more systemic options for breast cancer; fewer for gastric
             cancer, for example); due to the heterogeneity of tumors being treated in this
             protocol, the discretion of the treating physician in terms of timing of immunotherapy
             will be critical

        Exclusion Criteria:

          -  EXCLUSION FOR ENROLLMENT: Any other malignancy from which the patient has been
             disease-free for less than 5 years, with the exception of adequately treated and cured
             basal or squamous cell skin cancer, superficial bladder cancer, and carcinoma in situ
             of the cervix

          -  Pregnant women, nursing mothers, men or women of reproductive ability who are
             unwilling to use effective contraception; women of childbearing potential with a
             positive pregnancy test within 3 days prior to entry

          -  Significant cardiovascular abnormalities as defined by any one of the following:

               -  Congestive heart failure New York Heart Association (NYHA) classes II-IV;
                  patients with asymptomatic class I congestive heart failure (CHF) may participate
                  in conjunction with a cardiology consultation

               -  Clinically significant hypotension

               -  Symptoms of coronary artery disease

               -  Presence of arrhythmias in electrocardiography (EKG) requiring drug therapy

          -  Active and untreated central nervous system (CNS) metastases (including metastasis
             identified during screening MRI or contrast CT); patients with asymptomatic, treated
             metastases may be eligible if their lesion(s) have demonstrated stability over 2
             months

          -  Autoimmune disease: patients with a history of inflammatory bowel disease are excluded
             from this study, as are patients with a history of autoimmune disease (e.g. systemic
             lupus erythematosus, vasculitis, infiltrating lung disease) whose possible progression
             during treatment would be considered by the investigator to be unacceptable

          -  Any underlying medical or psychiatric condition, which in the opinion of the
             investigator, will make the administration of study drug hazardous or obscure the
             interpretation of adverse events, such as a condition associated with frequent
             diarrhea

          -  White blood cell (WBC) less than or equal to 2000/uL

          -  Hematocrit (Hct) less than or equal to 24% or hemoglobin (Hgb) less than or equal to 8
             g/dL

          -  Absolute neutrophil count (ANC) less than or equal to 1000

          -  Platelets less than or equal to 75,000

          -  Creatinine greater than or equal to 1.5 x upper limit of normal (ULN) OR creatinine
             clearance > 50 ml/min/1.73 m^2 for patients with creatinine levels above institutional
             normal limits

          -  Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) greater than or equal
             to 2.5 x ULN

          -  Bilirubin greater than or equal to 2.0 x ULN

          -  Positive screening tests for human immunodeficiency virus (HIV), hepatitis (Hep) B,
             and Hep C; if positive results are not indicative of true active or chronic infection,
             the patient can be treated

          -  EXCLUSION CRITERIA FOR TREATMENT: WBC less than or equal to 2000/uL

          -  EXCLUSION CRITERIA FOR TREATMENT: Hct less than or equal to 24%

          -  EXCLUSION CRITERIA FOR TREATMENT: Hgb less than or equal to 8 g/dL

          -  EXCLUSION CRITERIA FOR TREATMENT: ANC less than or equal to 1000

          -  EXCLUSION CRITERIA FOR TREATMENT: Platelets less than or equal to 75,000

          -  EXCLUSION CRITERIA FOR TREATMENT: Creatinine greater than or equal to 1.5 x ULN OR
             creatinine clearance > 50 ml/min/1.73m^2 for patients with creatinine levels above
             institutional normal limits

          -  EXCLUSION CRITERIA FOR TREATMENT: AST/ALT greater than or equal to 2.5 x ULN

          -  EXCLUSION CRITERIA FOR TREATMENT: Bilirubin greater than or equal to 2.0 x ULN

          -  Steroids are not permitted 3 days prior to T cell infusion and concurrently during
             therapy

          -  Uncontrolled concurrent 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

          -  Any non-oncology vaccine therapy used for the prevention of infectious disease within
             1 month before or after any anti-programmed cell death protein 1 (PD1) monoclonal
             antibody (anti-PD-1) dose

          -  After the T cell infusion, patients may not be on any other treatments for their
             cancer aside from those included in the treatment section of the protocol

          -  Coagulation 1.5 x ULN unless participant is receiving anticoagulant therapy as long as
             prothrombin time (PT) or a partial thromboplastin time (PTT) is within therapeutic
             range of intended use of anticoagulants