On High E, sure. You shouldn't be simulclimbing or cowtailing the first 60m pitch.
How about three people, one rope, no cows-tail tie-ins, no middle tie-in, no simulclimbing? Instead leader gets to belay ledge, anchors and ties in. Leader brings up second, who ties in to anchor with slings. Second then unties his end of the rope, coils it, and tosses it down to the third. Third ties in and leader brings him up to belay ledge. The leader had set the belay in the corner, so his second pitch was to traverse out right and up to the big triangular ledge on the GT.Remember, we're still talking about High E here. Before he gets too far, I call over (we were on The Last Will Be First) and ask him how he plans to get the rope back to the third person in the corner. I get a blank look. I then ask him how he plans to get the rope down to the third person on the last pitch, under the overhang and well in from the overhanging headwall, assuming the third survives their second pitch. I get an even blanker look, which I didn't think possible.
Some brain cells finally awoke from their stupor and they reconsidered, eventually opting to lower the third back to the ground. This was some time in the mid 80's. Stupidity on High E is, alas, hardly a recent occurrence.