End of June 2020, there was a planned Starlink (L9) mission on Jun 26, and OCISLY (Of Course I Still Love You, name of the vessel, really! Not making that up!) went out catch the stage.
Then a few days later, the GPS III Columbus mission was set to land on JRTI (Just Read The Instructions, the name is written on the deck in letters of fire 18 inches tall!).
However the Starlink mission was delayed and scheduled for after the GPS launch.
The question is thus, can the current ASDS (Autonomous Spaceport Drone Ship) OCISLY, stay out there, and spend the time between launches moving from one landing location to the other. Or is there mission specific equipment on the barges, such that OCISLY should come back, and JRTI should go out, and then OCISLY can go out again when the Starlink mission is back on?
I know that JRTI was upgraded when it was brought back from the West Coast with newer, bigger, more powerful thrusters for position holding. I have heard, without reference yet, that this helps with the location for Starlink missions, where the ocean currents are stronger than usual landing locations and the new thrusters are helpful.
Both ASDS barges are shown to have Octagrabber robots, which are used to drive under the landed stages, grab onto the booster around the engine mounts, and lower the center of gravity so as to secure the booster. This can be done before crew come on board, which in rough seas can be an issue. (At least two landed stages have been lost due to moving around the dock after landing successfully (Falcon Heavy flight three for example).