What is your approach to urate lowering therapy in patient with gout who is on azathioprine (for example, for transplant), where allopurinol and febuxostat are both contraindicated?

This is unfortunately not an uncommon scenario. As mentioned in the question, xanthine oxidase inhibitors such as allopurinol and febuxostat are contraindicated in patients on azathioprine or 6-MP and using them almost always leads to cytopenias due to azathioprine/6-MP toxicity (even in low doses)....