There is NO "max 2 wires per hole" rule. There are derating rules, and many will argue that pulling through holes in studs does not apply, but IMO that does not matter if you keep to no more than four cables to a hole with up to #10 conductors. There are code reasons for this which I won't go into right now.
I must ask, where are you drilling 2" holes in framing? 2x6 walls? I hope they are dead center.