I live in a 3 story 3-family house. In the back hallway, we each have a light on our floor as well as a switch (one per floor) but any of the switches will turn on/off all three lights. They always all work together.

I want to install a motion detector switch on the first floor so that when someone comes in the back door to the house/hallway, the hallway (all three floors) will automatically light. But I don't want it to prevent the 2nd and third floor tenants from being able to turn on/off the lights when they enter the hallway from their existing units. Can this work?

It will be easier to just ADD a motion detector triggered light, that will light up the back door and the hallway, enough so that the person entering has light until they get to the first-floor switch controlling the 3 floors of hall lights.

These existing lights are 3-way switches, so you would need a motion-detector that is also a 3-way switch. That is unusual; those are mostly wired as a single pole switch.