They have their eyes on Bahrain first as one of many steps, or dominoes, toward building a unified Shia Caliphate in the Middle East. I for one do not think Riyadh will let them go through with it. We may also see some very very curious military alliances against Teheran that we would have never thought possible in the past in that part of the world.
The Caliphate is by definiton Sunni. The Shia tradition has the mullah clergy rule the spiritual things, and earthly kings rule the secular world. Since 1979 there is the "velayat faqih" propagated by Khomeini, rule of cleric for the secular world within a quasi-modern Republican system.
Iran is a soviet-style "islamic republic" and not based on Shia tradition. It's a hybrid system of Bolshevist "world revolution" and a rather recent islamic ideology.
Since 1979 Iran's goal is to establish like-minded islamic Republics throughout the region, dominated by Iran. It's not the Caliphate and has not the traditional/aristorcratic trappings of it.
If the Iranians have a secure Bandar Abbas (port) why in the world would they (and the powers to be ) have their eyes on Bahrain? ya’ gotta’ know this- those Iranians don’t mess with Arabs and right now the country of Iran is total political upheaval and it’s not getting the press it deserves and the world is watching!