Is it possible to attach your own scripts to particle system particles, or add behaviour in other ways?

I'd rather not create a custom system from scratch, so the particle system seemed like a cool way to emit particles with all those options, that have behaviour as well.

They let us change physics related aspects of emitted particles and give us access to the collision function, but I can't seem to find a way to actually specify behaviour (with a script component for example).

A simple example case where I'd use this:

I turn physics on in the particle system. When the particle is created I keep track of when it was created.

Now when it hits some target object I simply read that value. The target object may be moving around so the order of particles hitting/being collected isn't guaranteed.