OP, what kind of sound are you trying to archieve?
The whole "use more OH and the close mics as a supplement" vs. "use more close mics" is truly a matter of taste, the song in question and how to get the best out of your kit, your room, the mics and the specific drummer.
For my part I'm a sucker for a dry early 70's drum sound with a wallet on the snare and sometimes some reverb to it and at times the toms. For that sound I find that the close mics has to run the show. I use mono overhead and let the pannings and sometimes bleed of the close mics make up for the stereo field and some level of ambience. For a start I used the mono overhead as a compromise out of lack of a matched pair of condensers but since then I slowly fell in love with this kind of setup and don't care that much about getting a matched pair.
I usually don't find bleed from other drums an issue, at times it's even an advantage, adding more texture and "sonic excitement" to the party - with hihat bleed in the snare being a notable exception, especially since I like to compress the snare quite a bit. My solution is to put a mic below the snare. Most mics will work but my favourite is my Sennheiser MKH-406 small diagram condenser. Flipping the phase of that and gating to tape to keep the snares from rattling too long. Sometimes gating again during mixdown since I'll rather gate a wee bit too little instead of missing out on subtle hits. This brings me really close to the snare drum sound I'd been dreaming about for years.
Another situation where I sometimes encountered in issue with bleed is when I want a really punchy and tight bass drum sound. It tends to excite the toms when there's a not a lot going on in the mics. In this situation just muting or spot erasing the iddle channels tends to help a lot. Usually not the OH though, usually sounds like crap if it goes in and out of the mix.
If you want a fuckpile of reverb and compression on the toms and snare something that can work is putting a gate before your reverb send. I find the built in gate in the Korg GR-1 spring reverb quite usefull for this and if you're working in a DAW I assume it's fairly easy too. Using only light compression on the snare and kind of medium on the bass drum and then parallel compression on the rest of the kit can work wonders for many kinds of sounds. If you're on DAW and not analog be aware of weird phasing issues with this though.
What mics are you using? My "standard setup" at the time is D112 on bass drum, M201TG on top of snare, Sennheiser MKH-406 below snare, Neumann KMS-105 on hihat (heavily EQ'ed to tape, pointing "out" towards the edge to avoid the air pressure of the HH opening and closing - although that can actually sound nice at times), Oktava MK-319 as mono overhead, 57's on toms, if out of 57's a 58 or cheap Sennheiser E-something on floor tom. Would love some MD-421 for the toms instead but money is tight and I get by with 57's.
If you'd like this kind of setup for your kind of music I have no idea but it works for me. Mind you I work on a quite forgiving medium in regards of drum sounds, would probably have to work differently if (god forbid) I had to record on a computer.
End of rambling, hope some of it was somehow usefull