Remember that there is NO pressure difference when firing two rounds instead of one. However, the force is doubled. The likeliest place to see damage is on the stock. The sideplates can cause a crack behind them. The tangs can cause cracks behind them. The wrist may crack. A well inletted stock which is then glass bedded will help keep these cracks from developing. Of course, the quality and layout of the wood is just as important.

Now for the metal. Some guns are made borderline in strength. I would be very careful with double rifles made from shotguns. There is a 3-5 times pressure difference and more force too. The old Flues shotguns sometimes crack the frame with modern ammo. This is especially true of gauges smaller than 12. In an overdesigned double rifle, the greatest problem would be with a gun off face. The looseness causes a hammering effect which greatly increases the force. Always fix off face guns. There is no "slightly" off face gun. Remove the forearm and shake the gun and this will let you know if there is looseness. It costs about $200 to have a double properly put back on face. Also, remove the barrels and thump the barrels with a pencil or something similar. Ringing is good. A dull sound is bad and means the barrels or ribs need resoldering. This most commonly happens when a gun is hot blued. It is too hot for the solder. Spanish guns may be brazed. They won't get loose in the ribs.

Personally, I am a rear trigger first kinda guy.