Unless there has been some major change to the ATX standard that I am unaware of, you should be able to use a modern PSU with high 12v and lower 5v on P4 motherboards in theory.
Back when the 20p power connector became a 24p power connector, the 4 extra pins would overhang when the power connector was properly seated. For a while, PSUs had 20+4 instead of a solid 24p connector.
However, chances are that the PCB area on the motherboard where the extra 4 pins would overhang, is occupied with components, making a 24p power connector physically not able to fit (best to not try to force or wiggle it in anyway if something is indeed in the way).
There are 24p to 20p adapters out there, but build quality may vary wildly. You may also need to find SATA to molex adapters as modern PSUs typically don't come with those anymore. My experience with such adapters is that it's usually the molex bit that may be crummy (always be alert when plugging one of those adapter molex connectors in). The sata bit usually fits relatively secured because of how SATA is designed.