Which schools, that give excellent need based aid, are still accepting apps?

Assume the applicants would have strong stats, such as ACT 29-31 and high GPA?

IIT give not need based aid but good merit. My son got offer with 30000$ renewable scholarship. But his stats higher than yours.

by “gives need-based aid” do you mean “pretty cheap for poor kids”?

West Point
Berea
Alfred
Westminster
New Mexico Tech
SD Mines
U of Maine at Orono
U of Wyoming at Laramie
U of Alabama Huntsville

Here’s the list from College Board of schools that accept later applications –
https://bigfuture.collegeboard.org/get-in/applying-101/late-applications

NMTech give not much need-based aid, but it does give merit aid starting at 3.0 GPA and 23ACT/1130SAT.

Mostly NMTech (like every public university in NM) has the Amigo/Legislative Scholarship for NM HS grads (including DACA and undocumented NM HS grads) that currently pays $1500/semester.

NMTech is great bargain for instate students since total COA (including books & personal expenses) is under $18K/year. Add in the Amigo ($3000/year) and guaranteed merit ($3000-$6000/year) and Tech is huge bargain.

OOS COA is ~$30K/year and OOS students are eligible for all merit awards, but NOT the Amigo.

NMTech automatically awards merit based on GPA + ACT/SAT scores. Applications accepted thru Feb 28.