The purpose of this study is to determine the optimal dose of ARGX-110 in participants with advanced malignancies and to assess efficacy of ARGX-110 (exploratory efficacy cohort 5 only).

Phase I study conducted in participants whose tumors express the target of interest. Pharmacokinetics (PK), pharmacodynamics (PD), biomarkers will be determined to support dose selection.

Phase II study conducted in Cutaneous T-cell lymphoma (CTCL) participants who are CD70 positive. PK, PD, biomarkers and immunohistochemistry (IHC) will be determined to assess efficacy.

Inclusion Criteria:

• Histological diagnosis of malignancy refractory to, or relapsing after standard therapy
• Solid tumors or T-cell malignancies positive for the CD70 antigen by Immunohistochemistry/Fluorescence-activated cell sorting (IHC/FACS) within 56 days prior to administering the first dose of ARGX-110. IHC criterion: greater than > 10 percent (%) of CD70 positive tumor cells
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1, or 2
• Serum albumin greater than or equal to (>=) 20 gram per liter (g/L) (solid tumor only)
• Ability to comply with protocol-specified procedures/evaluations and scheduled visits. In particular, the ability of the patient to undergo a tumor biopsy (optional for safety expansion cohort 4)

Exclusion Criteria:

• History or clinical evidence of neoplastic central nervous system (CNS) involvement
• History of another primary malignancy that has not been in remission for at least 1 year
• Systemic glucocorticoid administration at doses greater than physiological replacement (prednisolone 20 milligram [mg] equivalent) within 28 days of ARGX-110 first dose administration (for T-cell malignancies higher systemic dose can be allowed following discussion with Sponsor)
• Major surgery within 28 days of ARGX-110 first dose administration
• Unresolved grade 3 or 4 toxicity from prior therapy, including experimental therapy