We come across this every so often, we supply equipment that drives the LED signs you see by the side of the road.

From what we see customers doing/using, the most "common" way that these are constructed is with a common voltage and you switch ground in and out via a PWM, occasionally we've come across signs that are configured the other way, where the grounds are are common.

To be able to drive the common ground configuration, we have to supply an adaptor board which like StigOE points out, has the "opposite" FET configuration. (i.e P & N channel FETs swapped)

The alternative method, is to swap the LED's so that the A & K are the other way round, but that's not possible with SMD RGB LEDS because there's no rotational symmetry.