The best answer here is “yes.” As has been said elsewhere, for better or worse you are always changing your horse. The real issue is to make sure it’s intentional and in desirable ways.
Let’s pick a specific example, canter departs, for instance. If I get on a new horse, after he has become acquainted with how I want him to react to the individual basic aids, I will ask for the canter the “usual” way that I do. If it works, I’m in business. If it almost works, then we’re still fine. I will give him a second or even a third chance. If he clearly doesn’t understand me—if he has been taught some other combination of aids—there’s no point just shouting louder in an incomprehensible language. Then I will experiment with similar aids that he may be more familiar with. The point is to elicit the behavior I want and reward it. Once we are on the same page, I can gradually modify them until he responds to the “signals” that I want to use.
This all implies that you have a vision of how you want your horse to respond to you. If you aren’t sure what the best way to have him end up being is, it’s time for some professional in-person advice or a couple of rides on a “correct” horse so you know what you’re aiming for.