Squeeze/ compress/ shrink solid by pressing other solid into it?

Good evening folks,

does someone has a hint for me? I got this solid:

and i would like to press a cylinder into it like this:

So far so good, but i don’t want to perform a solid difference, i need the structure to be squeezed/ compressed/ shrinked. I don’t want to loose the detail of the structure - all the little combs. they should only disappear when they touch. probably i should perform like a squeezed sponge.

Any suggestions?

Thx in advance