Q. What if I want more punch? What should I move up to from 5.56mm?
If you are looking for more effective terminal performance you probably have to move up to 7.62 NATO or a 12ga shotgun. In 12ga, the Choke #00 "Precision Bonded" Buckshot appears to be among the best performers. Brenneke slugs are a good choice when penetration through intermediate barriers is required. Moving up to a 16-18" rifle chambered for 7.62 NATO might be a good alternative--as long as ammunition is carefully selected for optimal performance. In 7.62 NATO, the bullets with the best terminal performance include plastic tip bullets such as the 150 gr Nosler Ballistic Tip and 155 gr Hornady AMAX (they have dramatic fragmentation and usually maintain 13-15" of penetration in gel testing), as well as the 165 gr Sierra GameKing softpoint. Obviously, any of these combinations will be better for defeating barriers--particularly windscreen autoglass--than 5.56 mm, and accordingly should be more carefully deployed with an eye towards indoor overpenetration.
5.56 LC'00 (left) and 7.62 NATO Hirt (Right)