Withstand the higher pressure? What are you talking about? Can you explain your question further, as it does not make much sense.
As long as the rifle is chambered for a .223, a Remington SPS, or any other brand will not have any issues in terms of the "pressures" as long as you follow you handloading reference manuals or buy factory rounds. A 5.56 IS a military round (thicker case, and I'm told, loaded to higher pressures). The commercial rifles have .223 Remington. That is what they are designed to shoot. Don't mess around with this stuff.
When you passed your RPAL course, that was one of the important lessons they taught.
If you do happen to shoot the 5.56 ammo in your rifle, you may see immediate pressure signs, even to the point where the bolt may be stiff to open. There is plenty of cheap 223 ammo available on the market, buy the stuff by the brick load and have fun. Shoot what is stamped on the side of your rifle.