I think "too much" is relative and depends mainly on two factors in my opinion: if you're willing to throw more money away than you probably need to and if you think you'll be able to complete secondaries for 24 different schools in a limited amount of time without burning out.
Of course, the more schools you apply to, the somewhat better chance you have to getting an interview/admission if you have decent stats and all. But 24 might be slightly excessive and, in my opinion, should maybe narrowed down to about 20, so that you could use some extra time to focus on secondaries for schools at which you feel you have the best chance/are most interested in.
I haven't gone through the application process yet so this is all just an opinion. So it may be of more value to get opinions for those who've gone through it. Most of all, do what you think best suits you. If you have the time and money, applying to more schools doesn't hurt. You never know if one of the schools you left out may have accepted you. And also be sure that the schools you do aply to are not only top-tier.