I'm currently 17 yrs old (male) and my full-voice vocal range is from Eb2/E2 - G4/G#4. I regularly sing and try to healthily push the limits of my range with a vocal coach. My question is, do you think it's reasonable for me to expect to add two or possibly three semitones to the top end of my voice within the next year? My voice seems to have been settling pretty fast recently, and I would love to have the A's and A#'s that a lot of musical theater lead roles require.
OK this is a question that no-one here can answer because they do not know you, they have never heard you sing and they do not know how much effort you are putting into getting to the top/bottom of your range at the moment.
Pushing your upper limit further has the potential to be dangerous and/or damaging; you need to take the advice of a professional coach in a face-to-face situation.
You already have a good vocal range - don't ruin your voice by following advice from random users on the net however well intentioned it may be.