Food can do it.
I'm having a similar problem with Cora. We have a tentative diagnosis of kidney problems (based on the specific gravity of her morning urine), but she can't eat the kidney support diets that my vet carries. However, since the excessive drinking started roughly when I changed her food, I'm hoping that's the issue. The change back did not start well (soft poop), so I don't know yet if I'm right.
I agree: a vet visit is a good idea to rule out infection, kidney issues, and so on.
You might also PM Batmom, since her Zema has been showing similar symptoms, and she's done a lot of experimenting with food.