Step 1: The triad of cutaneous vasculitis, glomerulonephritis and peripheral neuropathy (often as mononeuritis multiplex) points to a small-vessel systemic vasculitis affecting skin, kidney and nerve simultaneously.
Step 2: This pattern is the hallmark of ANCA-associated vasculitis. Anti-neutrophil cytoplasmic antibodies (ANCA) are mainly IgG autoantibodies directed against antigens in the cytoplasm of neutrophil granulocytes and monocytes.
Step 3: Therefore the next investigation to confirm the suspected diagnosis is ANCA, which detects c-ANCA (anti-PR3) and p-ANCA (anti-MPO) patterns linked to conditions such as granulomatosis with polyangiitis and microscopic polyangiitis.
Step 4: The distractors are wrong because RA factor is for rheumatoid arthritis, HBsAg screens for hepatitis B, and MIF (migration inhibitory factor) is not the diagnostic serology for this vasculitic syndrome. Hence ANCA is the answer.