According to OALD both "all at once" and "at once" can mean at the same time.
I can't do everything all at once
I can't do two things at once.
Don't all speak at once!
These examples give me the idea that "at once" could be used when referring to a countable thing (in the latter example all is countable because it refers to a specific count of people, e.g. a class) while "all at once" is taken when referring to a non-countable thing (of course, everything could possibly be a countable thing).
Are they always used interchangeably or is one preferred in certain contexts?