A Study of DKN-01 in Multiple Myeloma or Advanced Solid Tumors

Inclusion Criteria: Part A: Patients with histological or cytological confirmed multiple myeloma or advanced solid tumors. For multiple myeloma, must have symptomatic myeloma as defined by the International Myeloma Working Group inclusive of measurable serum and/or urine monoclonal protein (M-protein) or for those without elevations they must have measurable increased concentrations of free light chains Part B: Patients with previously treated, histologically confirmed advanced NSCLC with progressive disease requiring therapy Parts A and B: * Refractory or intolerant to all standard/approved therapy(ies) * Patients with solid tumors must have one or more metastatic tumors measurable on computed tomography (CT) scan using Response Evaluation Criteria in Solid Tumors (RECIST) criteria * Radiation for symptomatic lesions outside the central nervous system (CNS) must have been completed at least 2 week prior to study enrollment * Treated brain metastases will be allowed, if they are asymptomatic. Patients must be off corticosteroids for at least 2 week prior to study entry * Eastern Cooperative Oncology Group (ECOG) Performance Status 0, 1 * Life expectancy of at least 3 months * Ambulatory patients greater than or equal to (≥) 30 years of age * Females with child bearing potential must have a negative serum pregnancy test within 7 days of study entry * Acceptable liver function, renal function, hematologic status * Urinalysis - No clinically significant abnormalities * Acceptable coagulation status: * Prothrombin Time/Partial Thromboplastin Time (PT/PTT) ≤ 1.2 x upper limit of normal (ULN) (unless receiving anticoagulation therapy - eligibility based upon INR) * International Normalization Ratio (INR) ≤ 1.6 (unless receiving anticoagulant therapy) * Receiving warfarin; INR ≤ 3.0 and no active bleeding * For men and women of child-producing potential, the use of effective contraceptive methods during the study and for women 18 months following the last dose of study drug * Available for the study duration and willing to follow procedures * Serum calcium: * Solid tumors only: within normal limits * Multiple myeloma: ≤ 11.5 milligrams per deciliter (mg/dL) Exclusion Criteria: * History of osteonecrosis of the hip or evidence of structural bone abnormalities in the proximal femur on magnetic resonance imaging (MRI) scan considered clinically significant or may impact the interpretation of the scan. Degenerative changes of the hip joint are not exclusionary * Unable to tolerate the confinement/noise of an MRI scanner or have any contraindication for MRI * New York Heart Association Class 3 or 4, cardiac disease, myocardial infarction, unstable arrhythmia, or evidence of ischemia * Have Fridericia-corrected QT interval (QTcF) \> 470 millisecond (msec) (female) or \> 450 (male), or history of congenital long QT syndrome. * Active, uncontrolled bacterial, viral, or fungal infections * Pregnant or nursing women * Radiation therapy, surgery, or chemotherapy, within 1 month prior to study entry * Previously treated with an anti-Dickkopf-related protein 1 (DKK-1) therapy * Significant allergy to a biological pharmaceutical therapy * History of major organ transplant * Had an autologous or allogenic bone marrow transplant, current acute leukemia, colon, prostate, breast or small cell lung cancer, osteoblastic lesions, concomitant disease known to influence calcium metabolism including hyperparathyroidism, hyperthyroidism and/or Paget's disease of bone * Unwillingness / inability to comply with procedures * Known infection with human immunodeficiency virus (HIV), hepatitis B, or hepatitis C * Serious nonmalignant disease * Receiving other investigational agent or have received other investigational agent within last 30 days or 5 half-lives, whichever is longer * Receiving lithium chloride (LiCl)