Can a light circuit be split out of the ceiling fan?
This is usually fine, just watch out for box fill

Adding extra lights to the light side of a fan+light circuit is fine.  The only real limit on how much you can add here (until you get to circuit ampacity, that is), is the watt rating of what controls the lights; this isn't an issue for switches, but can be a problem if there's a dimmer or combination light/fan control involved in the circuit.

The only other issue you can run into is box fill in the fan box; this isn't an issue for crossbar or saddle type fan boxes, but pancake boxes have essentially no usable fill, so if your fans are mounted to pancake boxes, you may have to change the box you're tapping power off at out for a different type, or tap power at the switch if switched-light-hot and neutral are both available there.