It depends, of course, on what “much” means. It also depends on the range.
So a kid who scores 1100 on a fall PSAT 10 as a sophomore can easily improve by 100 points to 1200 the next spring, which would move them from around the 80th percentile to the 90th. However, such a 100 point improvement from 1300 to 1400 would keep them within 2% of their original percentile, as they move from 97th to 99th.
However, the improvement from 1100 to 1200 is easier than the improvement from 1300 to 1400, and an improvement from the 97th percentile to the 99th is more profound than an improvement from the 80th to the 90th.
My point is that high scoring students tend to stay within a narrow range of percentiles because the cost of “moving” up each percentile is very high among students who initially score somewhere in the top 5%. However, for students who initially score in the middle, moving up 10 or even 20 percentile points is pretty common, especially for students whose school provides resources for SAT training, or whose parents can afford it.