How can I replace a 4-way mechanical switch with occupancy sensor(s)?
You could use some Insteon (or similar) home automation devices to have two motion sensors control the lights.

You'd need two wireless motion sensors and one dual-band switch. The switch receives the wireless signal from the motion sensors and activates the lights.

You'd then deactivate the other two existing switches (or add them back as "smart" switches, see below). 

When one of the motion sensors detects motion, it sends an "on" command to the switch. The motion sensor then starts an internal timer and if it does not see motion again before the timer expires, it sends an "off" command to the switch.

The only issue with this is that as you add additional motion sensors, you have a race condition to turn the lights off. This is likely not a problem for most scenarios, but if you have a super-long hallway or a giant warehouse that you're trying to cover with multiple occupancy sensors it'd be an issue. 

Hypothetically, lets say you have an infinitely long hallway with doors every 15 feet. Over each door is a motion sensor, they all control the lights, and they're all programmed to time-out at 1 minute.

Someone enters from one end of the hallway triggering sensor "A", which sends an "on" command and starts its internal countdown. As they walk down the infinitely long hallway, they trigger a new sensor every 15 feet or so, each sending its own "on" command. As soon as sensor A's one minute timer goes off, sensor "A" sends an "off" command, and the lights go out. 

This is where a more sophisticated commercial light control network is needed. But if you've just got three doors into a three-floor stairway, the two wireless motion sensors should work fine. If you expected people to linger in the hallway, you may have an issue, though you could just increase the time-out time to try to get around it.

You could also add additional Insteon light switches if desired to replace the existing switches--though the motion sensors would still try to turn the lights off on you!

NOTE: I've used Insteon products, but am not affiliated with Insteon or Smarthome in any way.