I've been playing the game exclusively solitaire so take this for what it's worth, but I'm also a pretty good rules lawyer and it's clear to me that you can't go back to the box unless you don't have enough cards to fill your slots.
In other words, you're stuck with your initial choices and it will take you time to level up with better stuff.
However, I think it's within the rules for the team at the end of a scenario to toss all your cards into one stack and take what you want, given that the intial owner has first dibs.
