One simple step to making an existing hole bigger
Next time you have to enlarge an existing hole — to replace an old lockset with a bigger one, for instance — try this trick:
Install two hole saws on a single arbor, one inside the other. The larger, outer saw should be the size of the new hole, and the inner saw should be sized to the existing hole and protrude at least half an inch beyond the outer saw.
Chuck the arbor into a drill and insert the smaller saw into the old hole. Then squeeze the drill trigger and carefully guide the saw through the hole to keep the drill on a straight, steady course as the larger saw cuts a new hole around it.