Phantom powered microphones have wide differences in power requirement: some work from 9 to 48 V, other don't work if powered with less than 40 V, some use really low power, some drain a lot of current.
I don't know the mic you intend to use, so I'm not sure it will operate with a lower than 48 V voltage.
Most of the microphones I've installed (and they are a really large number) worked flawlessly with a not standard 36 V dc supply (that happens to be the phantom voltage of the PA mixers I design and build).
Enclosed is a schematic I happen to have readily available: it's powered from a 12 V dc wall adapter, but adding other stages to the voltage multiplier it will operate from 9 V, or it will supply about 24-26 V dc if powered from 9 V.
regards
edit: disregard the preamp section, obviously...