SpaceX has several launch sites (and landing sites!)
In Florida they started at LC-40, and are working to activate LC-39A for launches, and LC-13 has been re-labelled LZ-1 for landings.
In California, they have SLC-4E for launch and SLC-4W for landings.
Boca Chica, Texas has seen little direct work yet, with the report being they will work on it post-LC-39A activation.
I will ignore Omelek (Falcon-1 launch site in the Kwajellin Atoll) since it is no longer in use.
One of the cost drivers on the space shuttle program was a standing army of staff, paid, regardless of flight rate that had to be maintained. SLS is likely replicating the jobs program aspects of this, for one launch every 3-4 years. SpaceX being dedicated to lower costs is clearly looking to minimize the standing army problem.
How has SpaceX structured their launch site teams?
LC-40 is clearly where most of the staff has been, since there has only been a single Vandenberg flight (Cassioppe) as I write this. However SLC-4 is due to get busier as there are a number of flights on the 2016-2017 manifest set.
When they launch from SLC-4 do they reuse the team from LC-40? Is it a separate team? What is the plan for LC-39A? Share the LC-40 team or have its own dedicated team? The structure of the launch team seems like it would be an interesting thing to understand.
The answer might include it, but a possible secondary question might be, how is their mission control team structured? One team to rule them all? Red team/Blue team? Or a problem to be solved when they have enough missions that they need more staff?