How would you manage gout with hyperuricemia >10 mg/dl despite the maximum dose of allopurinol plus probenecid and a prior allergic reaction to pegloticase?

I am not sure what dose of allopurinol the patient is taking, how long he was on pegloticase, and if he had MTX or MMF with it. I can usually reduce the uric acid level with allopurinol and febuxostat. The key question here is whether the patient is taking the drug daily or not.

I'm curious what the 'maximum' dose of allopurinol is. I've used as high as 800 mg a day. I also presume that the patient may not be compliant/taking the correct dose if their uric acid is not changing at all.