The ability to level up is determined by the star rank of Bronze, Silver, and Gold characters. Star to level caps only affect collectible characters. The bosses and NPCs that you meet on your way to victory can vary in level and star rank.

Here are the maximum levels a collectible character can reach based on star rank:
 
LEVEL 20
 
LEVEL 30
 
LEVEL 45
 
LEVEL 60
 
LEVEL 100