Anything can be done.
Question is, do you really want to do it?
Cost is always the 1st issue.
Complexity vs realibity is another issue
The only way to realistically aproach the design is to use momentary
push buttons, control and power relays.
All of these devices could be mounted in a common enclosure.
If you try to do the job with maintained 2-way, 3-way,
and 4-way switches, you will chase your tail till you drop just like
the guy they found dead in the round barn.
The finally figured out he ran himself to death looking for a corner
where he could take a leak.
My first job in the control business was for a machine tool electrical
control panel designer and builder the year Don Larson threw the
no-hitter in the series.
Been involved in the control business in one form or another ever
Personally, would touch this job as described with a 10 ft pole.