Yes there are several Hagia Sophiae. Beyond the two mentioned are one formelrly in Trebizond and another in Thessaloniki (St Gregory Palamas' cathedral, though the cathedral is now a smaller temple dedicated to him a few blocks south). There's also a Hagia Sophia in Washington DC - guess which jurisdiction.
Two asides: 1. as I recall from reading Taft and/or Lingas, Hagia Sophia and its daughters elsewhere did not originally have an icon screen, those becoming part of church architecture after the end of iconoclasm. As an aside, none of the Hagia Sophiae were made for the current liturgy, which allegedly only started being celebrated after the Latins were kicked out (Constantinople) or after the Ottomans were kicked out (Thessaloniki - in fact, one of the last pre-Ottoman Metropolitans complained about the current liturgy and the way it was celebrated in the early 1400s)
2. Stuart is right in the sense that the Ottomans did keep the building in good shape at great expense because it was the Sultan's mosque, whereas the Republican Turkish government has often treated ithe museum more as a tourist trap/cash cow, and has little incentive to fund the exepensive repairs it often needs.
