The document that provides the generally accepted definition for Phantom Power is IEC EN 61938. It's expensive, so I'll summarize. There are two standards:
- P48 must provide 48 VDC +/-4VDC @ 10 mA per microphone
- P12 must provide 12 VDC +/- 1VDC @ 15 mA per microphone
There was a third standard, P24, but I believe it was removed from the standard.
Some folks get a little 'generous' with the standard, and interpret it as ranging from 9V to 52V. You'll see this in various specifications. It is not entirely accurate, but as it turns out there is no harm done.
And in the real world most microphones will operate from a 15V phantom supply, even though it isn't a standard. I can think of two that simply collapse for lack of power (AKG C-414, AKG C-451), and one that gets downright nasty (Neumanm TLM-193, probably also the TLM-103).
The penalty will be reduced headroom.
Other than testing to satisfy my curiosity I don't use non-standard phantom supplies, and I always modify devices that switch phantom power in banks so I can kill it per channel. I also keep a stand-alone phantom supply around. I think it makes an audible difference, but I will concede that it is minimal.