A Study of DKN-01 in Combination With Paclitaxel or Pembrolizumab

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