Fleet Limits are described in the rules on the Kickstarter, but never really defined.
Each sector has a Fleet Limit, which is the number of players plus three. If a ship would be played into a sector which is at or above the Fleet Limit, deploy it into the sector with the fewest Opposition ships. However, ships may move into sectors that are already at their Fleet Limit, just not initially deployed there. Whenever a sector reaches its Fleet Limit, the sector panel is flipped to the Overrun side. An Overrun sector is flipped back to the starting side when there are zero Opposition ships in that sector.
How does a Sector reach its Fleet Limit? I would assume you compare the number of ships in a Sector to the Limit to see if you've exceeded it, yes? So, if you're playing a 5-player game, the Fleet Limit is 8. If there are 4 Opposition ships in a Sector, that Sector has not reached its Limit so you could deploy more ships there. If every player in the game wants to move into that Sector, there would then be 9 ships in that Sector, which would exceed the Limit, yes? That would mean that the Sector has been Overrun by player ships, I guess? Feels like I'm missing something.