Do you have an attic space? If so, you could install as many j-boxes as you want and then run new wiring in the attic. However, you don't then you might be looking at a surface mount install depending on where the additional lights are going to be.
If you are planning to use that existing circuit, then you need to figure out the existing load on the circuit. You will not be able to exceed 1920 watts on the circuit if it is a 20 amp breaker or 1440 watts if it is a 15 amp breaker. Watts=voltage x amps. If the only thing connected to the circuit are lights, then count up the wattage or the max indicated wattage on the fixture nameplate. If you have receptacles connected to the circuit, then you are going to have to take those into account as well. If there are receptacles, then you would have to assume a minimum of 180 watts per receptacle. Of course this would be un-realistic if you plan to plug in multiple higher ampacity devices such as drills, vac, etc. Basically, anything with a motor. If you plan to plug motor driven equipment into those receptacles, then add up the amps or watts associated with the equipment and use those values in lieu of 180 watts. In most cases, you could assume 180 watts for all recpectacles except for one, which you might want to assume 5 amps(600 watts). Reason being, is that in a one man operation garage, you can only use one power tool at a time. Of course there many variables and exceptions when it comes to each persons intended usage.
Once you get that figured out, and determine you can use that circuit, then the wire size is most likely going to be a #12 or #14. If the breaker is 20 amps, then you should use #12. If it is a 15 amp breaker, then you can use #12 or #14. of course you need to be aware of the panelboard location. If it is in close proximity, then these numbers apply, if it is over 100' (Circuit length) away, then you are going to have to take voltage drop into consideration.
Good luck!
