Yes there are. I eliminated these schools from my list of potential schools because they require these sorts of letters - any school for which a committee letter does not fully fulfill LOR requirements is one that is too peculiar and annoying enough for me to bother with. This is not a comprehensive list.
I'd love to know why the Florida schools are so into this kind of thing.
U of Alabama School of Medicine
"Strongly recommends" but does not require that applicants submit two additional personal letters of recommendation in addition to the committee letter
U of Central Florida
Requires two additional character letters (beyond committee letter), one of which can be from a peer
U of South Florida
Requires two additional character letters (beyond committee letter)
Indiana University
Requires one personal letter of recommendation "To be completed by a person who has known you for several years and who can evaluate your personality, character, and general fitness for the study and practice of medicine." in addition to academic letters of recommendation
U of North Dakota
Requires character letter. "These recommendations should include a letter from a peer, such as a roommate, spouse or friend and a letter from a science instructor."
U of Florida
Requires "1 character reference FROM A PEER (friend, classmate, co-worker)"
U of Wisconsin Madison
"One committee letter and one individual letter from a nonacademic source (someone other than a faculty or family member or personal friend)"