I've been thinking on this for days, but just as I made this post I think it dawned on me how to do it.
I have the yoyo on an extended axis. To get more rotation for the same distance pulled string (work/force), I will need an additional axis that will hold the gears that will help me get more leverage.
We can assume for the sake of ease that the axes are the same diameter. I will now attach the string (work/force) to the additional axis. This additional axis will have a gear that is, say, three times the circumference of the original yoyo axis. If the gear is connected to the yoyo axis, then when I pull the string the distance of the circumference of the original axis, the outer edge of the larger gear must travel further distance, hence, making the yoyo axis rotate three times the distance, or thereabouts, on a single pull.
Am I right? or close?