A really clean DA that actually puts out a decent amount of voltage into some sort of freakishly clean gain stage with an obscene amount of headroom that can handle said voltage going into an AD that can handle the incoming raised voltage.

Sans that, some sort of limiter. But if you want it louder, you're going to lose dynamic range... That's a given.

It might be helpful to know what kind of musical genre you are working with? You certainly don't want to over process operatic or, symphonic music. Rock 'n roll doesn't need to have obscene dynamics. So when losing some dynamics, you can pump it up. So, frequently, that's what you want. In order to obtain better apparent loudness, frequently, multi-band dynamics processing is utilized. Much in the same way as FM radio stations utilize. Then you can also throw in some broadband dynamics processing in addition to the multi-band dynamics processing. Allowing some peaks passed through without utilizing attack times that are too fast will preserve punch. In many instances, look ahead can be avoided to emulate analog processors. Faster release times will increase apparent loudness but can cause greater listening fatigue. Slower release times will reduce apparent loudness. So it's a juggling act. You don't get something for nothing. There are always trade-offs to contend with. Sometimes broadband is utilized before multi-band sometimes it's the other way around. Going overboard can take a good sounding product and turn it into doggy Doo Doo.

Some folks will swear by certain manufacturers software whereas others will swear by others. Other folks like to utilize actual analog processors in combination with software. Some just work in software. We don't all eat at McDonald's. Some folks go to Burger King, others go to Wendy's while yet others go to Jack-in-the-Box. Sometimes I like to buy them by the bag. Other times one is just fine.

Would you like pickles on that?
Mx. Remy Ann David

If you are going after that over compressed sound-top 40 try changing your technique of mixing and start by mixing through few compressors and limiters already on main output, each one tiny amount at a time, attack and release set to a tempo