I never mix two near-coincident pairs.
The underlying issue is that the signals from any microphones being summed together into the same channel need to either be fully phase correlated (usually by being coincident with each other) or different enough from each other that any undesirable cancellations are minimal and do not pose an audible problem. How to arrange things to achieve that is the key.
^This statement posted earlier is rooted in this kind of real world practicality, based on how tapers operate.
In contrast to that is what actually can be achieved within the realm of acoustic theory, but is not practical for tapers because it cannot be done reliably under the constraints in which tapers are operating. Carefully arranging and combining sources that are not fully phase-correlated in such a way that the cancellation and reinforcement works to advantage more than causes problems is possible. This falls in the realm of antenna theory, and specifically "beam-forming". Think phased-array sonar and radar systems. There are more complex multi-element microphones that truly harness phased-array beam-forming techniques that require careful computer modelling and testing during development to get them to work right, followed by being able to producing them within the tolerances required for proper operation. This is difficult, it gets messy quick. Tony Faulkner's "Phased Array" four microphone configuration Voltronic mentioned can be argued to be a very rudimentary form of something in this category.. arrived at empirically via the luxury of setting up, listening carefully, adjusting the setup based on that, listening again, readjusting, etc. Copying exactly that setup and using it in a different recording environment might work for tapers. But trying to do something similar but not exactly the same without the luxury of going back and forth between carefully listening and adjusting things until getting it to work with minimal problems is asking for trouble.
This is why a few of the more important aspects of any multi-microphone technique that might be deemed suitable for taper use is sufficient robustness and tolerance for variations in setup. Mixing two near-spaced pairs scores poorly by this metric, in the same way as does mixing a bunch of mics without carefully managing what's going on between them. In contrast. mixing spaced omnis with a coincident center pair scores very highly, which is why its an easy one to recommend. It is a configuration that is even more robust and tolerant of variances in setup than a two channel near-spaced pair used on its own, where getting the angle and spacing right between the pair is more important.
I don't think recording PA-amplified performances verses non-amplified sources such as an orchestra are significantly different in terms of how stereo microphone setups work, but I do think the acoustic situations are dramatically different. The same aspects apply, but the different acoustic situation calls for different solutions. The biggest difference is how a PA is carefully designed to project direct sound toward audience in a highly preferential way, shifting the critical radius of reverberation much farther out into room. An orchestra or other acoustic performance is much more omnidirectional and "illuminates" the room with sound very differently. Because of this, some taper solutions which work well for recording PA-amplified stuff seem ridiculous and strange in the classical recording world.
And likewise, some classical techniques are less appropriate for use by tapers. Mentioned previously in the thread was the relatively simple 4 microphone classical recording technique of a pair of spaced omnis flanking a near-spaced ORTF pair. Yes that can work for tapers. And it is attractive partly because it would seem to simply add the omnis to the "known-good" near-spaced stereo pair, which on its own is generally preferred by most tapers over a coincident pair. But without listening to get the spacing just right, a much safer bet is using a coincident pair in the center instead of a near-spaced pair. Once things start getting combined, you need to think about the entire system working as a whole, more than "starting with this and adding a bit of that". I'd also argue that the simple but specific combination of a coincident center pair and wide spaced pair provides advantages in terms of psychoacoustics. It's both safe and works well. Adding more mics beyond that gets trickier.
