Inclusion Criteria:  Participants have an inadequate response to receiving methotrexate (MTX) therapy Medically stable on the basis of physical examination, medical history, vital signs, and 12-lead electrocardiogram (ECG) performed at screening Have a diagnosis of rheumatoid arthritis (RA) (American College of Rheumatology [ACR]/ European League Against Rheumatism [EULAR] criteria 2010) Body weight within the range of 50.0 kilograms (kg) to 120.0 kg, inclusive, and have a body mass index (BMI) of 19.0 kilograms per meter square (kg/m^2) to 32.0 kg/m^2, inclusive All women must have a negative highly sensitive serum (beta-human chorionic gonadotropin [beta-hCG]) at screening  Exclusion Criteria:  Known allergies, hypersensitivity, or intolerance to any biologic medication or excipients of JNJ-67484703 Has a diagnosed or reported history or current signs or symptoms indicating severe, progressive, or uncontrolled hepatic, renal, cardiac, vascular, pulmonary, gastrointestinal, endocrine, neurologic, hematologic, rheumatologic, psychiatric, or metabolic disturbances Have other known inflammatory diseases that might confound the evaluations of benefit from JNJ-67484703 therapy Have a history of any clinically significant adverse reaction to murine or chimeric proteins, including, but not limited to, allergic reactions Have a history of or currently have felty's syndrome