What's the most efficient way to attach assets to 3D characters?

Example: I have a pirate character and I want to attach a parrot to his shoulder when the player attains a certain amount of points.
Problem: The character is rigged and the parrot will need to move along with the rig.

If I use a separate prefab, I do not think it’s possible to attach the parrot to the already existing rig. If I have the parrot game object mesh already on the character turned off, there’s some overhead to computate it anyway.

So what’s the usual method for attaching assets to an instantiated rigged 3D character prefab?

Take a look at these threads, they hold the answer:

Customise ANY character or model!

Shared skeleton and animation state