If you go to the TE website you should be able to see which schools still had open spots this spring for fall 2021 start.
My s23 is very unlikely to get TE unless he chooses a “less desirable” school. He’s a 3.4 possible music ed major who may also be interested in finance or something quirky. He doesn’t want healthcare, engineering, or business at this time.
ETA: list from TE openings from May 2021 (and beyond)
University of Saint Joseph
Oglethorpe University
Lincoln College
Saint Xavier University
University of St. Francis - IL
Illinois Institute of Technology
Rockford University
Saint Mary-of-the-Woods College
University of Detroit Mercy - FACHEX ONLY
Logan University
St. Louis University
Mississippi College
Pfeiffer Univeristy
Campbell University
University of Jamestown
Five Towns College
Mount Saint Mary College - NY
Alfred University
Ohio Christian University
The College of Wooster
Wilmington College
Bushnell University
Ursinus College
Wilson College
Mercyhurst University
Salve Regina University
Southern Wesleyan University
Johnson University
Bethany College
Schools added 5.5.2021
Bethany College
Louisiana Tech University
Regis College
Cazenovia College
Schools added 5.6.2021
College of Idaho
College of Saint Mary - Nebraska
Schools added 5.12.2021
Spring Hill College
University of Evansville
Newman University - KS
Southwestern College - KS
Aquinas College
Rockhurst University
Bloomfield College
Ohio Dominican University
York College of Pennsylvania
St. Mary’s University - TX
Bridgewater College
Schools added 5.13.2021
Monmouth College - IL
Valparaiso University
Albion College
Elmira College
St. Edwards University
Schools added 5.14.2021
Chestnut Hill College
Lawrence Universtiy
Washington & Jefferson College
Schools added 5.20.2021
The University of Lynchburg
Schools added 5.24.2021
Culver Stockton
Knox College
Schools added 6-4-2021
Holy Family University