My prefix may be any of various Rileys.
My infix is Riley's.
Most Riley riddles don't do my suffix,
but Riley riddles do my whole.
What am I?
Hint added later:
"My prefix may be any of various Rileys" — like Riley B. King, Dorothy Comstock Riley, or Jack Riley.
Hint added even later:
"My infix is Riley's" — could've been written "My infix may be of Riley", instead, had I wanted to make this riddle a little easier.