Definitely shell out the dough for a full work-up. My friend's cat started this and it turned out she was in renal failure. It can be treated if caught in time, but is fatal if not.
Have there been changes in appetite?
No changes in appetite. I have been working with him, since my husband and I both work out of our homes. My vet did a full physical and urine culture. All was well. I like the ideas about praise and new litter boxes. He is sitting here with me as I type. I love this cat and would just hate to see him go. My husband hates the vet bills.