Yes, Ivies will definitely take more than 1 student from a public school because it happens every year in nationally ranked high schools including the one in my area.
Now, if you are an Asian male from either CA or the NY tri-state area, and Harvard has already accepted a lacrosse recruit, a fencing recruit and an ISEF grand award winner, you are not likely to get accepted even with perfect scores/grades and a #1 class ranking. Could they squeeze in a 4th? Sure, but they have no incentive to since they have so many other “buckets” to fill.