Step 1: When skin, kidney and nerve are simultaneously attacked, the unifying explanation is inflammation of small blood vessels.
Step 2: The serological marker that pins down this family of disorders is ANCA, an IgG antibody aimed at neutrophil cytoplasmic proteins, giving the name ANCA-associated vasculitis.
Step 3: Rheumatoid factor lacks specificity, HBsAg checks for a viral cause that is less likely here, and MIF has no established diagnostic role, so ANCA is the test to order.
\[\boxed{\text{ANCA}}\]