Dave, or "Phineas" or "Tolstoy" or,
You may only complete one mission (that requires a test or combat) or one event per action. Missions which come into play completed may be scored immediately.
Just to clarify, Missions that carry the word "Condition" in front of them (and these are usually Influence Missions) may be scored when drawn, if the conditions have already been satisfied.
Fleet Captains Rules pg 28 wrote:
Some Mission Cards require you to create a specific set of conditions in the game.
These Mission Cards have instructions that begin with “Condition.” These missions work a little bit differently. To complete one of these conditional missions, you only need to match the current status of the game to the requirements of the mission. Sometimes, those conditions will be in place before the Mission Card is drawn. In this case, you can place it in your Victory Pile immediately.
Example: Starfleet Command has ordered an Expansive Survey. If you have explored six adjacent locations (i.e., the face-up Location Tiles are pointed toward you), then you have completed this mission and earned 2 VP.