Inclusion Criteria:

        In advanced esophagogastric malignancies:

          -  Participants with histologically confirmed recurrent or metastatic esophageal or
             gastro-esophageal junction squamous cell or adenocarcinoma or gastric adenocarcinoma
             with Wnt Signaling Alterations

          -  Participants must be refractory or intolerant to at least one prior therapy(ies) for
             metastatic or locally advanced disease

               -  If prior therapy consisted of palliative chemoradiation therapy, it will be
                  considered one line of therapy

               -  Prior treatment with paclitaxel as part of a definitive therapy regimen is
                  acceptable. Patients who are unable to receive paclitaxel for any reason will be
                  allowed to receive DKN-01 as a single agent.

               -  Prior treatment anti- programmed death-1 (PD-1)/ anti-PD-ligand 1 (PD-L1)
                  monoclonal antibody (mAb) is permitted in patients provided the patient's disease
                  is primary refractory, and the patient is not intolerant of pembrolizumab.
                  Patients who are not eligible to receive pembrolizumab will be allowed to receive
                  single agent DKN-01

          -  Tumor tissue for mandatory evaluation

          -  Must have one or more tumors measurable on radiographic imaging as defined by the
             Response Evaluation Criteria in Solid Tumors (RECIST). Patients with evaluable but not
             measurable disease per RECIST criteria may be enrolled with the approval of the
             medical monitor.

          -  Must be ≥18 years of age

          -  Performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) scale. A
             performance status of 2 on the ECOG scale may be entered upon the review and approval
             of the medical monitor

          -  Disease-free of active second/secondary or prior malignancies for equal to or over 2
             years with the exception of currently treated basal cell, squamous cell carcinoma of
             the skin, or carcinoma "in-situ" of the cervix or breast

          -  Acceptable liver, renal, hematologic and coagulation function

          -  For men and women of child-producing potential, the use of effective contraceptive
             methods during the study and for 6 months following the last dose of study drug

        Exclusion Criteria:

          -  New York Heart Association Class III or IV, cardiac disease, myocardial infarction
             within the past 6 months, unstable arrhythmia

          -  Fridericia-corrected QT interval (QTcF) > 470 msec (female) or > 450 (male), or
             history of congenital long QT syndrome.

          -  Active, uncontrolled bacterial, viral, or fungal infections, within 7 days of study
             entry requiring systemic therapy

          -  Known to be human immunodeficiency virus (HIV) positive, have hepatitis B surface
             antigen (HBSAg), or hepatitis C antibodies (HCAb) unless HCV RNA is
             undetected/negative.

          -  Serious nonmalignant disease

          -  Pregnant or nursing women

          -  History of osteonecrosis of the hip or have evidence of structural bone abnormalities
             in the proximal femur on MRI scan that are symptomatic and clinically significant.

          -  Systemic central nervous system (CNS) malignancy or metastasis.

          -  Clinically significant peripheral neuropathy at the time of study entry. Patients with
             pre-existing peripheral neuropathy will be allowed to receive single agent DKN-01

          -  Known osteoblastic bony metastasis

          -  History of known or suspected autoimmune disease with the specific exceptions of
             vitiligo, atopic dermatitis, or psoriasis not requiring systemic treatment.

          -  Clinically-significant gastrointestinal disorders, such as perforation,
             gastrointestinal bleeding, or diverticulitis.

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

          -  Treatment with surgery or chemotherapy within 21 days prior to study entry (42 days
             for nitrosoureas or mitomycin C)

          -  Treatment with low dose chemotherapy concurrent with radiation within 14 days prior to
             study entry

          -  Treatment with radiation therapy within 14 days prior to study entry

          -  Treatment with any other investigational agent within 30 days prior to study entry

          -  Previously treated with an anti-DKK-1 therapy

          -  Participants who have a history of hypersensitivity reactions to TAXOL® or other drugs
             formulated in Cremophor® EL (polyoxyethylated castor oil). Patients who exhibit these
             hypersensitivities will be eligible to receive single agent DKN-01.

          -  Significant allergy to a pharmaceutical therapy that, in the opinion of the
             investigator, poses an increased risk to the participant

          -  Treatment with corticosteroids (≥ 10 mg per day prednisone or equivalent) or other
             immune suppressive drugs within the 14 days prior to study entry

          -  Active substance abuse

          -  Receipt of any live vaccines within 30 days before the first dose of study treatment
             and while participating in the study

          -  History of (non-infectious) pneumonitis that required steroids or current pneumonitis

          -  History of interstitial lung disease

          -  Intolerance or severe hypersensitivity (≥Grade 3) to pembrolizumab and/or of its
             excipients