How can I combine multiple displace modifiers? I would like to create a scene where someone destroys an object (stone) with a pickaxe. With each hit the cracks are getting bigger until that stone will fall apart.

This is my plan for the cracks: I'd create 3 different images which show a procedure of these cracks. Then i'd use them in a displace modifier and try to adjust the timing when the pickaxe hits the stone.

But how can i combine two displace modifiers (i've used one for the stone itself, too) and make the cracks getting bigger and deeper?

Or is my way a bit too inconvenient. I think i could also try to use nodes, but i don't know which.
Though I think your project is better suited for shape keys here's a solution with displacement:

You can use multiple a displace modifiers on the same object, each one with a different image/texture as displacement and animate them separately.

Let's say you have 3 dsplacement maps:



By animating the strength on each one you can create transitions from one deformation to the next.