How do i make an object emit an object that is emitting objects? How do i get an object to shoot out an object that is shooting out objects with the particle system.
Blender 2.8 will have this feature, that will allow complex manipulation with particles (not only with particles):

https://www.youtube.com/watch?v=HQi2BqlQtnI

If you want to try something similar right now, you can try to use Animation nodes, but you need to know, that it has not so good performance as particles.