Inclusion Criteria:  Newly diagnosed or relapsing granulomatosis with polyangiitis according to American College of Rheumatology criteria, EMA classification algorithm and/or the 2012 revised Chapel Hill Consensus Conference definition. Aged 18 years or older Active clinical manifestations attributable to GPA  An inadequate response to previous standard of care therapy including  Both a combination of glucocorticoids plus cyclophosphamide and a combination of glucocorticoids plus rituximab Or an inadequate response to a combination of glucocorticoids plus rituximab and a contraindication to cyclophosphamide  An inadequate response to treatment defined as follows:  A progressive disease unresponsive to previous standard of care therapy after 12 weeks of treatment Or a lack of response, defined as < 50% reduction in the disease activity score, after 12 weeks of treatment Or a persistent active disease attributable to either a vasculitic or a granulomatous manifestation of GPA that requires the maintenance of corticosteroids ≥ 7.5 mg/day of equivalent prednisone after ≥ 12 weeks of treatment. A stable dose of oral glucocorticoids of ≥ 7.5 mg/day of equivalent prednisone within the 4 weeks before enrollment. Pulses of methylprednisolone (1 to 3 pulses of 7.5 to 15 mg/kg each; ≤ 1000 mg) are allowed if necessary, according to severity before starting the experimental treatment. A stable dose of conventional disease-modifying anti-rheumatic drugs (cDMARD) within 4 weeks before enrollment if the patient is currently treated with a cDMARD Patients must have the ability to understand the requirements of the study, provide written informed consent prior to participation in the study (including consent for the use and disclosure of research-related health information) and comply with the study protocol procedures (including required study visits) Patients must have an affiliation with a mode of social security (profit or being entitled)  Exclusion Criteria:  An allergy or hypersensitivity to monoclonal antibodies or either of the study drugs (rituximab, abatacept or tocilizumab) or to their excipients A previous treatment with a combination of rituximab plus a cDMARD, with abatacept, or with tocilizumab A contraindication to a combination of rituximab plus a cDMARD, to abatacept, or to tocilizumab (including an ongoing infection; history of recent cancer <5 years before enrollment, except for cured non-melanoma skin cancer); pregnancy; and breastfeeding. Patients with severe vasculitis manifestations that requires plasma exchange therapy including severe renal failure with a creatinine level ≥350 µmol/L or severe alveolar haemorrhage Patients with vasculitis in remission Patients with symptoms attributable to chronic and non-active GPA Patients with severe cardiac failure defined as class IV in New York Heart Association Patients with acute infections or chronic active infections (including HIV, HBV or HCV) Patients with active cancer or recent cancer (<5 years), except basocellular carcinoma and prostatic cancer of low activity controlled by hormonal treatment Pregnant women and lactation. Patients with childbearing potential should have reliable contraception for the 12 months duration of the study Patients with other uncontrolled diseases, including drug or alcohol abuse, severe psychiatric diseases, that could interfere with participation in the trial according to the protocol Patients included in other investigational therapeutic study within the previous 3 months Patients suspected not to be observant to the proposed treatments  Laboratory parameter exclusions  aspartate or alanine aminotransferase (AST/SGOT or ALT/SGPT) > 5 times upper limit of normal Platelet count <100.000/mm3 White blood cell count <2000/mm3