In order of the way your questions were asked:
1. Add a 4th axis, yes.
By the time one crafted up all the electronics and pneumatics for the type of 4th axis used on my machine, it is easier and cheaper to find a used one and plug and play.
2. Which design are you referring to?
3. Haven't found any.
You probably could do a crude adaptation of a manual rotary table with a servo motor fitted to it. You could use a servo based encoder to simplify feedback and then use gear ratio based math to coordinate table motion.
For true and precise accuracy, you'd rather have the encoder fitted directy to the table via direct drive or zero backlash gears.