My opinion:
You can connect 4 speakers to 2 channels *if* the amp can handle the impedance of the combined (parallel or series) speaker pairs.
You didn't provide any details about your speakers or amps so I can't tell if this will work in your case.
I assume you are talking about 4 coax or full-range speakers, and not separate drivers in an active arrangement?
You mainly lose the ability to adjust the level between the combined speakers (like front-back fade). If this is OK with you, then feel free to try it.
It works best if you are combining identical speakers with identical impedances, other wise you can get some unwanted interactions that affect sound.
If you have the budget, then I would add the extra amp and give each speaker its own channel. This will give you the most control over you system.