ive had success in keeping them longer by sectioning them up into smaller portions and ensuring that they are as dry as possible before refridgerating them. a paper towel in with each ziplock bag helps in absorbing the moisture. also buying the greens uncut or 'fresh' versus pre-bagged will give you a bit more time usually. there are demos on how to prep meals that'll help you out.
That's what I do too. When I get new greens I wash them and then cut the stems out (they go to the bugs) and then chop them into hand sized pieces that will fit into a ziploc with a folded paper towel. They tend to keep for at least a week or two that way.