At a time vs At one time

at a time—

1. simultaneously:

• We present items, three at a time, and ask informants to pick the one that is most different from the other two.

2. is used of a particular period of time:

• She grew up in the capital at a time when its artistic life was at its most brilliant.

Note: The expression does not correlate in meaning with the phrase at times—now and then:

• Our work is cut out for us, even though it can be heartbreaking at times.

at one time—

1. = at a time 1:

• Let’s start the dance again, all at one time.

2. at some time in the past:

• At one time most school teachers were men.