PCA9685 Switching

Is it possible to switch the +12 vs the ground with this board?

It would require design changes to do this. The on-board fets are N-Channel, which is often referred to as a “Low Side Driver”. The design would require P-Channel Fets for a “High Side Driver”. N-Channel has the advantage of working at many voltages because it simply makes a connection to ground. High-side would be limited to the input voltage, which is rated for 12VDC. They both do the same thing, but in different ways, the Low-Side Driver is more flexible since it does not care as much about the voltage range (within reasonable limits). I have not seen an application in which this board will not work for low-side switching instead of high-side switching, but please feel free to comment. Sorry for the long delay, I am the only one here who can comment on this particular design.