I know plenty of people with 32s at top schools. Not prodigies, either. Improving the score certainly wouldn’t hurt any, though.
People around here love to exaggerate. 32 ACT is within the middle 50% at HYPS. It is, however, in the bottom quartile for MIT and Caltech. Of course, they don’t play Division I football … 
But being in the middle 50%ile means you have the same sub 10% admission chance as other students…
Just throwing reality on the fire - a 32 with full need does not automatically open doors to Ivy’s or Stanford. It would be misleading and dangerous to OP to imply that they are likely to get in with that. I am seeing a rash of kids thinking “I’m poor with good grades - I’m in wherever I want to go!” It is harder than that. Disappointment to follow.
There are other meets 100% need schools the OP should consider.
^ Then throw the names out there.