Adding a Torque Box
A torque box is a chassis strengthening component that ties the frame rail to the outer rocker panel. Basically it's just a triangular box that keeps those two pieces from moving independent of each other.
The early model 65-66 convertiles got two, one on each side, coupes and fastbacks got none. In '67, fastbacks and coupes got one on the drivers side. The 1968 Mustangs were the first year to get torque boxes on both sides for all body styles. Up till then, only the convertibles got both of them. Ford should've done this in the first place, but I assume it was a cost-cutting measure to leave it off the fastbacks and coupes for as long as they did.
The beauty of this is that the '68 chassis are the same as the '67, so it should fit just fine. Except that almost everyone who makes this upgrade reports having to really struggle with fitting the new metal because after years of flexing, abuse, use, and general entropy, there's a little slop in the chassis interfaces where the torque box gets installed. There's always one guy who says his torque box just "dropped right in", but that's the exception. I'd say prepare for a fight.
Free advice: get the two-piece box. Yes, it costs more, but it fits better and makes installation easier. This whole effort (prep, prime, fit, weld) took about 20 hours over the course of a week of stay-cation at home.
Here's the torque box on the drivers side, installed at the factory during the Johnson Administration: