Step 1: The scenario is inadequate disease control on methotrexate-based therapy in rheumatoid arthritis. The management logic is a treat-to-target escalation of disease-modifying drugs.
Step 2: Because methotrexate is working as the backbone but is insufficient alone, the next move is to layer on a second conventional synthetic DMARD. Sulfasalazine is the time-honoured partner in such combinations, frequently as part of triple DMARD therapy.
Step 3: Persisting unchanged on methotrexate and steroids ignores the lack of response, and merely changing the methotrexate from tablet to injection is a pharmacokinetic tweak, not a true treatment intensification.
Step 4: Biologic anti-TNF therapy is generally reserved for after conventional combinations fail and is co-prescribed with methotrexate rather than started as standalone monotherapy at this stage. Therefore adding sulfasalazine is the appropriate next step.
\[\boxed{\text{Add sulfasalazine}}\]