Where are you located? Will your chickens be outside EVERY DAY for most of the daylight hours? Year round? Then yes, you could fit more. But if you live somewhere where it gets cold, hot, snows or rains a lot, and chickens will be spending a fair amount of time inside, then your probable limit is 2. When you crowd them, it gets harder to maintain a clean, unsmelly coop and you could end up with featherpicking and cannibalism problems. Just say'n.
I have 4 standards and there is NO WAY they could live in a 2x4 space. I know this because that was the size of their brooder and they were practically ON TOP of each other. It just wouldn't work long term.