In order to make it a fun experience hunting for multi-part antiquities there should be something in the game itself that points you from a find to the next lead location. Perhaps a hint in the note you get back from the antiquities guild or something found buried alongside a fragment.
Unless I am mistaken there's no such thing atm and just looking at the game itself we're left to the vanishingly small chance of stumbling upon all the leads needed to complete a multi-part antiquity.
It seems to me like a design flaw that if I want to have a decent chance of ever completing one I have to rely on info gathered by the player base and published through add-ons , websites, in chat etc.. I think the quest for multi-part antiquities can potentially be an interesting game play experience in its own right, but atm it doesn't feel like it.
Please stop making requests for game features. ZOS have enough bad ideas as it is!