Particle Properties on Particle Properties

Is there a way to have an unbaked object with particles properties (hair) and have it emitted by another object as a multiplier of itself using yet another set of particle properties. If so, how?

I tried doing it but the object seems to be baked as one frame therefore when the emitter produces more copies of it, the objects are simply stuck in one posture instead of working as a physics-based object. When I bake the first simulation of