Actually I'm pretty sure absolutely nothing will happen even if you claim every piece of Arc equipment. I'm putting this in [good spoiler tags], Gold, unless you know about the Arcs and who owns them:
On a side note it seems the author arbitrarily assigned the stars the Greek lettering names. Wikipedia has it differently.
So if you realise, you have multiple weapons and multiple protective equipments. Not only is it highly unlikely you actually need more than one Armament 99.9% of the time, the inability to equip possibly more than two Armaments at the same time meansthe rest will be sitting in your storage doing nothing. Eg. You can equip Zeta and Alpha at the same time maybe, but what will happen to the unused Epsilon?
Ownership of more than a single Arc is also highly unrealistic because of the sheer number of Enemies you're going to have to fight to get to one. V7 should already indicate how difficult it is to obtain even one.
And taking ownership into account, the easiest six of the Seven Arcs have already been obtained. Four of them are being wielded by Kings, no less. One has been locked up and the last one is unreachable in the near future. To own more than one you'd need to figure out how to kill a King...