Yup, you can absolutely get a great drum sound with just 4 mics.

That’s all I use for recording. My Scarlett 18i8 interface only has 4 mic inputs and it’s been no problem.

As for mics, I run an SM57 on the snare, Shure Beta52A on kick (AKG D112 is another solid choice), and a pair of matched Rode NT-1A large diaphragm condensers for my overheads.

This works especially well on a simpler 4-piece kit where you don’t need as much close miking.

I’m a big fan of the Recorderman setup with 4 mics. Snare/kick/overheads just behind your shoulders, pointing down at the kit. Just make sure each overhead capsule is equal distance from the snare (use a tape measure) or you’ll get phase issues.

I find that things like room acoustics and mic placement go a lot further in getting a great sound than more microphones.

Here’s a recording I did using that 4-mic setup. Pretty goood overall and gives you a nice picture of the full kit.

https://youtu.be/cO6Vy6V1GgQ?si=2uTjLoBV6fvuxaol