It's not possible. Pretty annoying, yeah. Either make a new profile on your PS3, or try an in-game workaround.
The way I do it is like this: go to the item management screen, store all weapons/supplies and buy useless stuff until your money count is as low as possible. Discard the useless stuff, discard or keep track of how much extra ammo/healing you have, and your item box is free for use. Then just pick Chapter 1-1 and play normally.
In RE6 you also keep all the points ($) and skills that you've unlocked, even if you start a brand new game. --- And this time!