So I'm aware that attunement cannot be applied to more than one copy of a magic item, I.E. two rings of protection. Does the same rule apply to magic weapons that require attunement as well?
You can only attune to one copy of a magic weapon at a time.
The relevant rule on attunement states:
Additionally, a creature can't attune to more than one copy of an item. For example, a creature can't attune to more than one ring of protection at a time.
Magic weapons are no different from other magic items in this regard; you can only be attuned to one copy of a particular magic weapon at once.
You can speak with your DM about said topic. If allowed, one could have another weapon type crafted with the same magical properties as the initial weapon of choice. Mind you, you can't benefit or be penalized from multiple similar properties. If a weapon creates an on going effect, one presumes it would restart the effect upon every hit or not at all. If a magical property pushed the target away, then your additional attack would not have a viable target.
The easiest way to invent a new item is to tweak an existing one. If a paladin uses a flail as her main weapon, you could change a holy avenger so that it's a flail instead of a sword. You can turn a ring of the ram into a wand, or a cloak of protection into a circlet of protection, all without altering the item's properties. (DMG pg. 284)
Just remember your attunement limit of 3 items.