Inclusion Criteria:

          -  Histologically proven, relapsed/refractory metastatic colorectal cancer

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

          -  Measurable disease per RECIST 1.1 criteria

          -  Participants in the Dose Escalation Phase must have had recurrence, progression or
             intolerance to standard therapy consisting of at least 2 prior standard regimens
             (containing a fluoropyrimidine plus a platinum analogue and/or irinotecan) for
             metastatic disease. Participants in the Cohort Expansion portion will be allowed to
             participate after 1 prior standard regimen. Those who are inappropriate candidates for
             or have refused treatment with these regimens are also eligible. No more than 5 prior
             therapies are permitted. Patients previously treated with MGD007 on Study Protocol
             CP-MGD007-01 and who did not develop antibodies to MGD007 while on the CP-MGD007-01
             study, may be enrolled. Patients that were previously treated on CP-MGD007-01 will
             only be treated on this study once MTD/MAD has been defined.

          -  Availability of sufficient tumor specimens to enable retrospective determination of
             gpA33, CD3, PD-1, and PD-L1 expression

          -  30 participants in the Cohort Expansion portion must have lesions that are accessible
             for paired biopsies with acceptable clinical risk in the judgment of the investigator.

        Exclusion Criteria:

          -  Symptomatic central nervous system (CNS) metastases. No concurrent treatment for the
             CNS disease; no progression of CNS metastases on MRI or CT for at least 14 days after
             last day of prior therapy for the CNS metastases; no concurrent leptomeningeal disease
             or cord compression

          -  History of known or suspected autoimmune disease with certain exceptions

          -  History of prior allogeneic bone marrow, stem-cell, or solid organ transplantation.

          -  Major surgery, systemic anti-neoplastic therapy, or investigational therapy within 4
             weeks

          -  Radiation therapy within 2 weeks

          -  Systemic corticosteroids (≥ 10 mg per day prednisone or equivalent) or other immune
             suppressive drugs within the 14 days

          -  History of Grade 3 or greater drug-related diarrhea/colitis during treatment with
             checkpoint inhibitors including anti-LAG-3, anti-PD-1, anti PD-L1, or anti-CTLA-4
             antibodies

          -  Clinically significant cardiovascular disease; gastrointestinal disorders; pulmonary
             compromise; viral, bacterial, or systemic fungal infections

          -  History of positive testing for human immunodeficiency virus or history of acquired
             immune deficiency syndrome

          -  History of hepatitis B or hepatitis C infection or known positive test for hepatitis B
             surface antigen, hepatitis B core antigen, or hepatitis C polymerase chain reaction.