To this date, SpaceX currently has 2 droneships to land their first stage rockets on. Their first ever droneship, names "Just Read The Instructions" (JRTI) is currently located on the West coast for launches from Vandenberg in California. It was originally positioned on the East coast for launches from Florida, but was moved because they'd finished their second droneship - "Of Course I Still Love You" (OCISLY). "Of Course I Still Love You" is currently active on the East coast for Falcon 9 and Falcon Heavy launches from Historic LC-39A and from Space Launch Complex 40 (SLC-40).
Elon Musk stated on Twitter this morning, that "Side boosters landing on droneships & center expended is only ~10% performance penalty vs fully expended.", which means that if there were to be a mission with an expended core stage, SpaceX would need 2 droneships for each of the boosters. Musk then went on to say that "A third is under construction" and would be completed with the name of "A Shortfall of Gravitas". This third droneship would be positioned on the East coast to support the high launch rates of their Falcon 9 and to support the duel ocean landings for the Falcon Heavy side boosters.