I think that any ring made after the crafting of the One Ring would still be under the dominion of the One Ring. Sauron had a rightful claim on all the elven-rings because his craft-lore was used in their making.
Quote:
But (Sauron), finding that he was betrayed and that the Elves were not deceived, was filled with wrath; and he came against them with open war, demanding that all the rings should be delivered to him, since the Elven-smiths could not have attained to their making without his lore and counsel
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I can't find any 'defense' against Sauron for their full ownership of the rings except for hiding them and not openly using them when Sauron held the One Ring. Apparently, the elves understood the concept of copyright laws and patents.

So as long as Sauron existed, any ring made would fall under his dominion.
Now, any rings made after Sauron's destruction...I don't think that any of the elves left in ME held the knowledge of ring-making. An interesting thought!