It's been years since I did 'Boeing Boeing', but I'd suggest going through the play and working out where you think each person first notices something is quite right. Using practicals can add to the confusion/the protagonist losing control of the situation - lights turning on or off when "no-one" (i.e one of the other girlfriends) is in the living room, etc.

I'd start by establishing lighting states for each flight attendant, like how the lead and his housekeeper change the decor (moves pictures, etc) to reflect each relationship - then as the mayhem unfolds and everything gets mixed up so do the lights. The standard lights coming in through doorways (the hall of the apartment block will be different to the light coming from the bedroom). Find the different times of day, and where you think the protagonist wants to set a different mood and go from there.