Three sided play should be entirely possible, and sounds fun!
The game mechanics should not be affected to any great degree.
I see the game progressing for each individual action as though the game is only a one on one.
Players would need to simply keep the bigger picture in mind as the game progresses.
Whether there is two or three players one full ...
You should continue from the previous phase.
Travelling always occurs at the end of any phase in which either blip pile is empty, thus you finish resolving the current phase, then resolve travelling.
After this you would continue from where you were up to in the normal order of the game.
I do not have a specific rules reference for this, except that ...