Would you start potassium citrate in a patient with recurrent nephrolithiasis of unknown stone composition who has hypocitraturia and alkaline urine pH?

I would be slow to start potassium citrate for a patient with alkaline urine and stones of unknown composition. Alkaline urine predisposes to calcium phosphate kidney stones, and potassium citrate would likely make the urine more alkaline and worsen the formation of calcium phosphate stones.

First, ...

I agree with the approach and priorities enumerated by Dr. @Dr. First Last, though some of the over the counter citrate supplements, like Moonstone/Stone Stopper, can be used to supplement citrate with minimal impact on urine pH in patients with ongoing stone activity and low urine citrate.