waves - Do photons occupy space?

Total noob here.

I realize that photons do not have a mass. However, they must somehow occupy space, as I've read that light waves can collide with one another.

Do photons occupy space? and if so, does that mean there is a theoretically maximum brightness in which no additional amount of photons could be present in the same volume?

Answer

However, they must somehow occupy space, as I've read that light waves can collide with one another.

That's not true. Yes, light waves can "collide" and interact with each other (rarely), but that itself doesn't imply that they need to occupy space.

It's not even entirely clear what it means for a subatomic particle to occupy space. A particle like a photon is a disturbance in a quantum field, and is "spread out" across space in a sense; it doesn't have a definite size in the same sense that a macroscopic material object does. But you'll probably agree that, if it's possible to make any sensible definition of "occupying space" for a subatomic particle, it should involve preventing other things from also occupying that same space. Photons don't do that. They're bosons, and as a consequence of that they are not subject to the Pauli exclusion principle, so if you have a photon occupying some space (whatever that may mean), you can in theory pack an unlimited number of additional photons into the same space.