You can own any number of items (but only one copy of each). It is not limited only to what you can equip. So when you find armor in a chest and already have armor, you still get to keep the armor you got, you just won't be able to equip it until next scenario. Actually, since you can only equip items in between scenarios, even if you weren't wearing armor, you'd still have to wait to equip the armor you just got.