Do you have any other...

[subhajit123]

Can I use singular countable nouns after any other? And are the following sentences grammatical?

1- Do you have any other book?

2- Do you know any other doctor?

3- Is there any other way to do this?

 

[J&K Tutoring]

All three are grammatically correct, but your #1 and #2 are not typical. In those situations (and many like them) we expect to be able to choose from among several options, unless we are looking for something very specific, or if the first item offered is so terrible that we would accept every alternative. Even at that, it's very unusual to ask about a single book.

Your #3 is natural as written.