So far "schwa" has not informed us with a clarification as to his actual application so everything is a bit speculative still .
That said, Rudy4 brought up a good point and it is an issue even without full phase cancellation, because you can get comb filtering issues without total cancelation.
Recording an acoustic instrument in an inclosed space has potential phase "distortion" comb filtering issues even with only one mic, let alone multiple mic's . Now while this phase distortion can actually be pleasing (ie. good "stereo" recording ) phase is non the less distortion and increasing the number of mic's increases the potential for increased distortion issues .
And while there are numerous ways to minimize these phase issues and multiple mic techniques are routinely used by experienced engineers. The reality is that increasing the number of mic's increases the potential for phase issues plain and simple. So answer to the original OP , absolutely one can indeed throw too many mic's at a recording.
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