The character should have a single state machine.
Animations should be controlled by the character state so they don't need their own character-specific state machine except as part of a generic animation system.
Status variables (health, ammo, invincibility timer, inventory, etc) are part of deciding which state to transition to but not state machines in themselves.
If there seem to be a need of multiple state machines this usually means the character should be split up into different entities, the AI simplified, or both.
The main reason for this is the K.I.S.S. (keep it stupid simple) principle. Multiple state machines on an entity will too often create unexpected combinations of states, often soft-locking the game in a way that is hard to trace and debug.
If, for example, state machine A has 12 states, state machine B has 5, you have 60 possible combinations that may happen, many of which are probably invalid. Trying to figure out which one of those 59 other possible combined previous states is responsible for entering the current combination becomes a much bigger task.