You absolutely cannot raise your stem too high. Chances are that your stem is already at its maximum height on the fork's steerer tube. I can't imagine there being a bunch of steerer tube sticking out above your stem where it clamps to the steerer.

The guideline is that you want the stem to be about 3mm higher than your steerer tube.

Have you flipped your stem to get more vertical handlebar height? That's one thing you can do, provided that your bars haven't already been flipped as such.

If you are dead set on raising handlebar height, and you don't have any fork steerer tube left, then you need a new fork.

Alternatives to raising handlebar height include getting a shorter stem. Sounds like you're having issues reaching the handlebars, correct?