Explode particles at end of particle life

I have a particle system emitting Suzannes, and I would like each Suzanne when it dies (or just before) to explode.

Now, I applied a particle system to the Susanne that the particle system emits, and added an explode modifier. Unfortunately, what happens is that when the original Suzanne explodes, all the emitted Suzannes explode at the same time.

I want them to explode when they dies, so I get a series of exploding Suzannes.

Is that possible to do?