Drum machine sweetening is basically voodoo
So yes, the basics first: Compression, distortion, gating, EQ. There is no set recipe, you just have to experiment with what effects processors you have, what settings, and what order. I find the lower-fi, older 80's processors often do wonders here. Yamaha SPX90!
Imo machines that produce simpler, less complex tones take to processing better and seem to produce crisper results. The Arturia DrumBrute (the OG one) might be a hated machine, but damn it takes processing well and it can deliver all the crack and slap you want.
Transformers. Yep, the magic of transformers can really make a difference here. If you can get your hands on a JHS Colourbox V2, that device can do wonders (miracles?) for drum machines.
Individual outputs. Rules out cheaper machines but you pretty much have to process sounds individually. You can still do this with single-out machines (you just have to process and track each instrument separately in multiple passes) but the workflow for individual outputs is
dramatically easier. There's a separate thread around here, but if you have the space/budget for an analog desk so you can route all your individual drum machine outputs to channel strips, you get EQ, single-knob compression (on some models), FX sends, and bus routing and that is the key to getting things sounding right. The bus routing is important in case you need to process groups of individual instruments together (such as your hats and cymbals). Dialing everything in on a console where everything is within reach and not buried in menus or mousing about really helps the creative process imo.
These techniques go all the way back to the early days of the 808 and how those producers made it hit so hard. It takes a lot of experimentation.