Definitely, you can have as many as you want. But they only hold 1 slice each. Lots of players like to stack them , some have up to 10.
Personally I have only 2 pizza boxes. But I bought 3 cold pizza slices as well, which recharges every 24 hours. This works better for me because I have bad luck finding lots of slices in the game. But I never have any energy problems now. You just have to figure out what works for you.