Kitties
Penn State (easter Mountain Lion)
Northwestern (Wildcat)
Houston (Cougar)
Kansas State (Wildcats)
Kentucky (Wildcats)
Arizona (Wildcat)
BYU (Cougars)
Auburn (Tigers)
LSU (Tigers)
Missouri (Tigers)
Birds, Amphibians, Reptiles, and Bovine
Maryland (Testudo)
Florida (Gators)
TCU (Horned Frogs)
Iowa (Hawks)
Kansas (Jayhawks)
Texas (Longhorns)
Colorado (Buffalo)
The Maryland/Florida/TCU makes for a neat trifecta. Those are the core. Fewer birds than you might expect, but maybe one day Illinois will join them. Colorado/Texas make for a pair.
Furry friends
Wisconsin (Badgers)
Minnesota (Gophers)
Michigan (Wolverines)
Baylor (Bear)
Georgia (Bulldogs)
Mississippi State (Bulldogs)
Cincinnati (Bearcats) - not a cat, apparently!
So many critter teams - I decided to go with "fur" as a theme. Is a bearcat snuggleable? I dunno. But I bet a Mountaineer could make a jaunty hat out of it, so let's put em here.
Jobs/Occupations
Purdue (Boilermakers)
Nebraska (Husker)
Indiana (Hoosiers)
Oklahoma (Sooner)
Oklahoma State (Cowboys)
WVU (Mountaineers)
Texas A&M (aggies, but also Reveille)
People, its made of people.
Warmongers
Vanderbilt (Commodores)
Tennessee (Volunteers)
Michigan State (Sparty)
Texas Tech (Red Raider)
UCF (Knights)
Ole Miss (Rebels)
One could argue some of the Jobs pod could be here, but we've got to have some balance.
Other
Ohio State - Buckeyes
Illinois (formerly Illini, possibly belted kingfisher?)
Iowa State (Cyclone, but also Jack?)
Alabama (Crimson Tide, but also elephant)
Arizona State (Devils)
Utah (Utes)