OP you have some CCs best long-time posters telling you the same thing:
- tippy top colleges will not be impressed by you adding AP summer courses
- “1 or 2 tiers lower, e.g. Columbia or Cornell” is simply wrong- they are the same tier. One tier lower is a college in the 15-20% admit level. Two tiers lower is the 25-35% admit level (indicative %, not exact, obvs).
- Do something with your summer that speaks to what you are interested in. Do summer courses ONLY if they link to your larger narrative arc. To quote the Dean of Admissions at Princeton: we don’t care what you do with your summer: we care that you do something and we care about what you do with it after the summer.