Any recommendations for an RPG system with extensive character customization supporting a wide variety of body types (including non-humanoid)?

I have an idea for campaign in my head but I need to find a good system to run it. Main thing I want is a system that would allow people to play humans, humanoids, and non-humans, with enough system and character customization depth to make the differences feel interesting and meaningful. Basically, if a player wants to be a fire magic-wielding phoenix or a psychic cat, they should be able to do that.

Ideally the system would also have at least some level of support for typical fantasy adventuring stuff (dungeon crawling, combat, social intrigue, etc.)