Just a few points of discussion, Iloyzmandias ...
Mongul, while usually portrayed as Superman's superior after his initial appearance, was actually far below Superman when he first appeared. Mongul could not defeat the Martian Manhunter who was guarding Warworld's crystal key, so he blackmailed Superman -- the one being guaranteed to defeat J'Onn -- to get the key for him. It's ABC logic. Superman > Martian Manhunter > Mongul, therefore, Superman > Mongul in Mongul's first book. Mongul was mysteriously beefed up to Superman-plus levels after that story which was never explained.
When Superman faced team-empowered foes like Amazo or the Composite Superman (later Xan aka Amalgamax, which was a much cooler name), the circumstances usually kept Kal-El's own powers out of the mix.
Amalgamax only had the powers of Supergirl, Mon-El, and Ultra Boy, not Superboy, and even then, this was in their early teens when their powers were duplicated in the statuettes. I believe Superman was pretty even with Amalgamax until he used Triplicate Girl's power to outnumber him for might. The other Legionnaires tended to be irrelevant unless their specific talents were taking advantage of Superman's weaknesses (e.g. Element Lad creating kryptonite). Look at the statuettes the LSH gave as a gift. Superboy wasn't amongst them as why would they give a statuette of the recipient? Also, Kal would have to be in on the gift if he himself stood in the duplicator ray. No, Superboy's were not in the Composite Superman's arsenal of duplicated powers.
Amazo didn't have Superman's powers due to the same red radiation robbing Superman of his necessitating his use of the Supermobile, so the android was using MM's powers instead. A later Amazo encounter in an annual book does suggest he was using Superman's real powers then.
Superman was not even with Amalgamax. Meach had the power of 3 Kryptonian level heros. He surely wasn't 3 times stronger than Superman as he boasted, since they WERE teens, but he was still clearly stronger, and even without Element Lad's power, Superman didn't have a chance in a straight fight.
Good point about Mongul. If he could have beaten the Martian, he would have, and we saw how Superman kicked Jo'nn's butt even without using his fire weakness. But unexplained power-up or not, he was stronger than Superman in later encounters.