How could i do this ? (Rigid body cell fracture)

I have a mesh that i want to break / collapse progressively hit by hit, like if we were mining on it.
I setup the first break with cell fracture + rigid body that work greatly to make just one part of the rock fall and keep the rest static but don’t understand how could i set up a second one etc… I explain :

To make a part of the rock break at a 2nd hit, i have to select it and make it collapse with cell fracture, then being rigid body active Dynamic at the wanted moment. So i have to make the original complete rock mesh to go out of the scene at this moment, to keep only the little broke parts. But when i animate this Big part to make it diappear from the scene it totally screw up the rest of the simulation, making all my elements centered on the same mesh and not interacting properly anymore…

How could i setup a second cell fracture happening later on a mesh that is part of a first one? And then a third, etc ?
Ty by advance for any help