Immunosuppressive therapy - does it work for all kinds of arthritis?

No. Immunosuppressive therapy is not used for osteoarthritis which is the most common type of arthritis. At least at this point, the factors that lead to osteoarthritis seem to be more degenerative in nature than autoimmune. Overactive immune systems play the major role in rheumatoid arthritis, psoriatic arthritis, lupus and others.