You said it's a "little politer", is there any more polite form than "～ます"?
yes. 飲まれます、お飲みになる、お飲みになります、お飲みになられます、お召しになる、blah blah. I think you need to remember only ”ます”.
That's a lot @_@
You're right, I think I can only cope with the common terms at this stage, and thank you again! どうもありがとう！(btw, is it possible to say "またどうもありがとう！"?)
Oh, I see, thank you! XD (sorry, I couldn't reply directly to your reply)