Part A of this trial consists of 4 treatment arms of DKN-01. It is a dose escalation study in patients with multiple myeloma or advanced solid tumors. Patients must be refractory or intolerant to all standard/approved therapy(ies). At each dose level, 3 subjects will be treated. If none of the 3 subjects develop a dose limiting toxicity after a minimum of 4 weeks of treatment, subsequent dose escalation will proceed according to the same schedule. Part B consists of dose confirmation in patients with NSCLC. Patients must be refractory or intolerant to all standard/approved therapy(ies). Approximately 15 patients may be enrolled in Part B.