Other posts while typing.. before I launch into an essay, I'll just say I totally agree with Ed and lastubbe considering the way most 4 channel mic mixes are done around here- which is generally two seperate pairs of mics, each setup as an individual stereo pairs, mixed together. That's not what I'm suggesting in any of the scenarios below...
[edit- and Brian is spot on in suggesting that direct and simple ways of improving your two channel recording technique are more appropiate than adding more mic channels! What follows is more about why one might use 3 channels, and sort of assumes that you are already getting satisfactory results with two!]I am intrigued by the 3 mic stereo option. How far apart would you place your mics? With the mixing would you somehow divide the center between the left and right?
The mixing is simple: center panned center, Left/Right panned hard-left and hard-right. The main thing to adjust is the center level, and optionally EQ.
As for mic setup, a basic approach is simply adding a center omni without changing your typical L/R main pair setup. That's a 'safe bet' way to try this as you can simply toss out the center if it adds nothing useful. A center omni helps the low bass range, often compensating for a low end roll-off response of the directional main pair. It can also help solidify the center of the playback image and provide a way of adjusting how much ambience you want in the mix.
The next step down the 3 channel path is to think about adjusting the main L/R pair with the addition of the center in mind. That usually means adjusting the L/R pair to be angled or spaced wider (or both) in such a way that might compromise the main L/R pair by itself, but benefit the resulting mix with the center added. When I started doing this I sort of worked my way farther towards a dedicated 3-channel setup, so if it didn't work out I still had something that wasn't over compromised in the L/R pair alone. But the results were encouraging, which gave me the confidence to try more outlandish setups, some of which completely sacrifice stereo compatibility of the L/R pair alone for optimizing the 3-channel setup.
One of the 'totally safe', but really useful and conceptually simple optimized setups is three spaced omnis. Addition of a center omni allows you to space the L/R pair wider than you would otherwise without fear of getting a 'hole in the middle'. In fact, the safest bet is to try this by spacing the L/R pair twice as wide as you normally would. In that case you can always throw away one of the outside mic channels and substitute the center for it instead and you’ll end up with your original 'safe' L/R stereo omni spacing. You can put all three mics in a line, or move the center one forward a bit like a classic Decca tree. Works anywhere spaced omis are appropriate and is almost always better in my experience. I've never once had it turn out worse. I just did this for an outdoor festival last month and instead of the typical 3' two channel omni spacing I use there, I spaced the L/R pair 6'. Super win. No down side other than running an extra channel and figuring out how to do the spacing.
Optimizing a setup with directional mics gets tricker, as the best results begin to require setups that don’t work as well with just the L/R pair alone. You can go seat of the pants by simply going a good bit wider with the L/R pair. If you are using three directional mics instead of a center omni, it may help to think of the Left-Center pair as one stereo set which happens to be immediately adjacent to the Center-Right pair, with the two linked-up in the middle. Michael Williams has extended the Stereo Zoom technique based on this concept. He calls the optimization of the overlap between each recording segment ‘critical linking’. There are papers about it and an active web page configurator at his website to help determine good setups based on the recording angle you want. I don’t know it off the top of my head, but I’ve posted links to his site in the microphone section here if interested.
To go whole hog, I’ve tried an Optimum Cardioid Triangle setup a few times which uses a center forward facing cardioid and Left/Right supercarioids facing directly to the sides. Setting up that one gets odd looks and lots of questions from fellow tapers! Obviously something like that is only usable in 2-channel stereo if you mix the three resulting channels together.. but OCT is primarily designed as an optimal way for sending each channel to individual speakers for 3 channel stereo playback. And so it goes down the rabbit hole..
To sum it up- If you want to try 3 mics, adding a center omni, or using three spaced omnis is a good safe start. Generally from that point on, the greater the risk taken in compromising the two channel setup, the greater the potential reward of using three channels to best effect. And I think that is really the ‘Achilles heel’ of most of the typical 4 channel mic setups which others have found lacking in the end. With a few exceptions we can discuss, most of those setups are not really optimized to be mixed together. If the resulting mix does work out well, it’s more or less something of a happy accident.