Study to Assess Safety and Efficacy of Anti-Interleukin 6-receptor (IL6R) Nanobody in Rheumatoid Arthritis (RA) Patients

Inclusion Criteria: * Body mass index (BMI) \<35.0 kg/m2 * Diagnosed with rheumatoid arthritis (RA) according to the 2010 European League Against Rheumatism (EULAR)/ American College of Rheumatology (ACR) criteria for at least 6 months prior to randomisation * Treatment with methotrexate (MTX) for at least 12 weeks prior to screening, with at least 4 weeks before screening at a stable dose, that will remain stable throughout the study period. Inadequate response or or intolerance to disease modifying antirheumatic drugs (DMARDs) (including MTX, where a patient may remain on treatment with %TX at a lower dose for improved tolerance, but with reduced effectiveness) * For patients (men and women) of reproductive potential, use of an acceptable method of contraception for the duration of the study. Female patients must be willing to use appropriate birth control measures that would prevent pregnancy starting from the time of signing the informed consent until 90 days after the last dose of study drug is administered * For single dose part: Disease Activity Score using 28 joint counts (DAS28) score \>= 2.4 * For multiple dose part: DAS28 score \>= 3.2 * For multiple dose part: swollen joint count \>= 3 Exclusion Criteria: * A documented history of an autoimmune disease other than RA (other than secondary Sjögren's syndrome) * Functional class IV by ACR classification * Any new/additional biologic DMARD therapy, cytotoxic drugs and immunosuppressants within four weeks prior to screening, and between screening and Day 1 with the exception of ALX-0061 * Suspicion of active tuberculosis verified by quantiferon test and abnormal chest X-ray * Female patients who are pregnant during the study, or are breastfeeding * History of anaphylactic reactions to protein therapeutics * Participation in an investigational drug study within 60 days prior to drug administration except for the patients who participated in the single dose part of this study and who are eligible to participate in the multiple dose part * Donation of more than 300 mL of blood within 60 days prior to drug administration * Malignancy, or prior malignancy, with a disease free interval of \<5 years after diagnosis and intervention except curative treatment for non-melanoma skin cancer or resected carcinoma in situ * Any current or recent (within 4 weeks prior to first dose) signs or symptoms of infection that requires parenteral antibiotic administration, any known active viral infection (hepatitis B virus \[HBV\], hepatitis C virus \[HCV\], human immunodeficiency virus \[HIV\]) that would impair the participation in the study * Major surgery (including joint surgery) within 8 weeks prior to screening and hospitalisation for a clinically relevant event within the 4 weeks prior to screening * Any other disease, metabolic dysfunction, physical examination finding, or clinically significant laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or renders the patient at high risk for treatment complications * Administration of a live, attenuated vaccine within 1 month before dosing with ALX-0061, or anticipation that such a live attenuated vaccine will be required during the study or within 60 days after the last dose * For multiple dose part: contraindication to MRIs or the use of contrast agents for MRI scanning