Another approach sometimes is to paint the effect directly over the animation's frames, if you use a paint program with particle brushes, such as Dogwaffle. www.thebest3d.com/pdpdor/tutorials and www.thebest3d.com/dogwaffle/whatscool has examples

But it can't do all imaginable particle types, especially sophisticated emitters. For that, Particle Illusion may work better, perhaps./ Another  one is Magic Particles by Astralax, see http://thebest3d.com/astralax/index.html

If you need a tool for compositing, perhaps with greenscreen, Dogwaffle Pro can help there too.