Final answer:
The most likely additional finding in a patient with positive ANCA, focal necrotizing vasculitis, and pulmonary nodules indicative of a vasculitic syndrome such as Wegener's granulomatosis is hemoptysis.
Step-by-step explanation:
The patient described has a positive antineutrophil cytoplasmic autoantibody (ANCA) test, renal biopsy showing focal necrotizing vasculitis, and pulmonary nodules on chest X-ray. These findings are highly indicative of a vasculitic syndrome such as ANCA-associated vasculitis, which can include disorders like Wegener's granulomatosis.
Given the clinical picture, hemoptysis would be the most likely additional finding. Hemoptysis refers to coughing up blood from the lungs and is a common symptom associated with vasculitic diseases due to inflammation and bleeding of the small vessels in the lungs.