BJ...
Wire size, insulation rating, temperature rise...
Coil saturation at 60Hz normally never a concern.
Normally the designer spec'd small gauge high-temp conductors with insulation rated to 150 Centigrade. Even so, there's only so many amperes you can shove through the transformer.
This limit is found when the B-B is trying to bump/buck a lot of current a minimal voltage.
Normally this is no sweat since the typical B-B transform is 277 down to 240 ... or 208 up to 240. You do note that the RATIOS are the SAME. Stacking two such common B-B permits 277 to buck down to 208; which was a proposition on another thread.
------
Thus you have multiple limits: how much the magnetic circuit can handle and how much the conductors can handle. There are frequency limits, also, but at 60 Hz you not be troubled.