Is it possible to have multiple people work on the same Unity project at the same time?

Thank you!

I would recommend you setting up an external Version Control System, for instance Subversion (SVN).

Yes, definitely possible. But you do have to be careful.

The key things IMO are:

You must use a version control system. Having used perforce, SVN, and git with Unity, my own recommendation from those would be git (because branching is so easy, see below).

Try as much as possible to have people working on different parts of the project, to minimise how often they are changing the same files. Merging of changes is possible but can get fiddly.

As much as possible, have people work in their own branches and only push their changes to the mainline branch when they know it’s stable.

The above points are general. A Unity-specific one is that it helps if one puts as much as possible into prefabs rather than scene files. Scene files are difficult to merge, so it’s best if they are as minimal as possible. Rather than having objects in your scene, use a scene manager which creates the objects from prefabs when the scene starts.