That big sound is a combination of things. And it's an illusion.
If what you mean by "really good sounding acoustic kit" is that you have your drums tuned to ring a lot and sound really open and big, that's part of the battle. New heads can be a big help. If you have a really good acoustic kit with 6 year old hydraulic heads and the o-rings and the napkins and the gaff tape and the moongel all over the place, try getting rid of all that stuff. It will make your drums sound bigger.
Mic placement is a critical issue. If you're not sure about it, experiment. Grab one microphone. The best one you have. ONLY one microphone.
1. Put it somewhere
2. Record something
3. Assess what it sounds like
4. Put it somewhere else
5. Repeat steps 2 through 4
Barring anything silly like putting an expensive mic in harms way where it's going to be damaged, you should be able to find a few spots where you get a good, balanced representation of the entire kit. You'll find other spots that might leave something to be desired, but they might bring something else to the table. An overhead mic above the drum kit can give a good representation of the entire thing. Putting the same mic say 2 to 4 feet in front of the kit looking slightly over the kick, kind of aimed at the rack tom(s) and/or snare can give you a good representation of the entire thing. But it will sound totally different than the overhead. Try the mic from either side of the kit. Try it behind the kit. If you get too much of some things and not enough of other things, keep moving the mic until you get a good balance of everything.
The beauty of doing this is that once you record the same kit with the same player in a different room (or even a different spot in the same room) the very best, ultimate mic placement that you found earlier won't always work. Developing your ears to hear what sounds good or not and moving the mic to get there is a valuable skill to develop rather than just relying on formulas or pictures of how someone else did it.
Once you've exhausted this approach, you might want to try more than one mic. A pair of overheads is common. Some people like x/y stereo. Some people like spaced pairs. These aren't the only options. You might like to have a combination of the sounds coming from above the kit and off to the side of the floor tom. This is starting to sound a bit like the Glyn Johns/Recorderman/John Holmes paint by numbers mic scheme. Hey, if it works for you that's fine.
Once you start to combine 2 mics, check to make sure they're both in phase with each other. If they sound wonky and phasey, adjust the placement very slightly to get rid of the phase cancellation. You will never completely get rid of all of it, just go for a happy balance. Find the best compromise you can.
Once you get up to 17 microphones on the kit, each mic will want to eat a portion of the signal coming from all the other mics. Compare this recording to the one you did with just one mic. Ask yourself which one sounds bigger.
Consider the sound of the room. Is it a church? Is it a walk in closet? Is there lots of concrete? Taming nasty reflections in a less than ideal recording space might be beneficial. Room acoustics. Heavy curtains. Bass traps. Packing blankets. Carpet. Important things to consider. It's not quite as simple as getting the room live or dead.
Putting up a room mic might help to add a sense of space and depth. People make odd suggestions for room mics. This really expensive ribbon, or that super nice condenser set to omni might make a nice room mic. Better yet, those are probably the mics you would have good luck with using as overheads or overall kit pickup. Some people that do this recording stuff for a living would be inclined to use some of the cheapest, nastiest sounding mics available to them as room mics. Placement is critical of course. Here are some descriptions I've seen:
- an SM57 in front of a gobo in front of the kit, aimed away from the kit
- a pair of karaoke mics in ORTF placed above and behind the kit in the corner where the wall meets the ceiling
- a mic out in the hall to the lounge (ie. room mic not in the same room)
Basically what room mics are supposed to do is give a sense of space. They aren't intended to pick up the direct sound of the kit. They're intended to pick up reflections. Annihilating the output of these mics with a compressor might be an interesting idea as well. If they don't sound ANYTHING like your kit, that's probably okay as long as you can blend a bit of this signal with the proper drum sounds and get some kind of a sense of space or bigness happening. Hopefully with very minimal phase artifacts. If you want to try a really nice mic from farther away, not in a weird position or with anything funky going on, that's probably okay too but it might sound a bit more like a simple delay. If that's what you want you can probably just play around with adding delay to your sounds, but that's usually not what room mics are about.
Parallel compression on close mic sources like kick and snare is another thought.
But getting back to the core of the original question, it's mostly about whether or not the kit sounds truly big in the room. The right heads, tuning and room acoustics are the most critical factors. If you end up finding a bunch of tricks to make the drums come out sounding artificially bigger, hopefully there's room in the mix you're trying to achieve for that kind of approach to actually work.