The highest I';m able to play without any issues is high F#.
With an F# key or without it?
Try this. First off, you have to blow differently for altissimo notes. No fingering in the world is going to help you unless you squeeze the airflow a bit by raising the back of your tongue towards the roof of your mouth as you blow. Just try this sitting where you're sitting. Pretend you're blowing a note and then slowly raise the back of your tongue up towards the roof of your mouth. You should get a sort of whistling affect by doing this. Now you're ready for the horn.
Use your octave key, front F, right hand 1 (F) and side Bb. Squeeze off the airflow and see if you can get F#3 this way. When you can do this, let go of right hand 1 (F) and voice it up to G. Add the side C and voice it up to G#. Then for A, I'd go with octave, left hand 2&3, right hand 1,2&3 (OXX-XXX).
Once you get the notes, then ya gotta work on making them sound good.