Unless the speaker designer envisioned an external crossover being used, you are altering what they designed. So it's a guess as to what will happen. It may work fine or you may end up with a speaker sounding entirely different from what you had before, and from what the designer intended. It may or may not be an improvement.
Now if you multi-amp with an active crossover, that's a different story. That doesn't seem to be the intention from your post however. It seem that you are still planning to use the single amp.
Now if you multi-amp with an active crossover, that's a different story. That doesn't seem to be the intention from your post however. It seem that you are still planning to use the single amp.