Can an object occupy a space which is occupied by another object?

Answer 1

No. With large objects it is easy to see that they cannot occupy the same space.

Smaller objects can appear as if they can occupy the same space but, at the molecular level they cannot. For example, you can dissolve sugar in a glass of water and it looks as if they are both occupying the same shape - but they are not.

At the sub-atomic level, the Pauli exclusion principle prevents objects (electrons) occupying the same space.

Answer 2

It depends on what you mean by object and space. Is a black hole an object ? Then the answer is yes. If two black holes merge they will occupy the same space (and not take up twice the volume).