My regular weekend gig has me multitrack all the live shows I do. I usually run from 8-24 tracks and when there are drums I will run between 5-8 mics on the kit. Kick, Snare, HH, OHL, OHR, FTOM,RTOML, RTOMR. Since they are the loadest you usually get a pretty clean sound, without much bleed through from other intruments. The OH is where you get bleed through if the bass or guitar is close.
So, hell ya, multi track them drums. The control you will have afterwards is worth the effort. If you don't have alot of channels to use you can get away with 3 mics; Kick, OHL, OHR or 4 mics; Kick, OHL, OHR and Snare. For 5 I add HH.
Enjoy!