Wanting to top 'Star Trek', the producers will pull out all the stops and after a heavy commercial campaign, the sequel will be a huge hit. The third movie (a direct follow-up to the events in part two) will suffer from being a rushed production with heavy studio involvement and an unfinished script (why wait three years between movies when you can just film them back-to-back?). Also, at this point, Abrams will be losing interest in the franchise as it slips further and further away from his creative control. He may hire some lacky he worked with on Alias to direct part three and/or four.
While resolving the plot threads started in the second movie and making a huge chunk of change, the third will be a critical failure. After a long hiatus, the creative team may come back together to do one more sequel (with these actors). This movie has the double duty of trying to be a franchise revival and a loving send off --just in case it doesn't succeed.
Also, the stars who have had the biggest careers outside of Trek may want to be
killed off for real (or at the very least,
put on a bus) in order to get out of future movies. Likely suspects include: Chris Pine, Zachary Quinto, Zoe Saldana, Anton Yelchin, and Simon Pegg. Pine and Quinto in this scenario would just get bigger paychecks. Saldana and Yelchin both have promising careers outside of Trek. As they continue to become "serious actors" they may drift away from the series. Pegg seems the most likely to depart since he plays such a minor role and has so many other projects to work on instead.
Around this point we may get a spinoff TV show with John Cho as the captain of the Excelsior, or whatever, but at that point it will be less like keeping the franchise alive and more like sucking the marrow out of its bones. This may sound pesssimistic but seriously --what studio nowadays would OK a movie like The Voyage Home? The original team could get away with something like that since it could be done relatively cheaply. Because ofthis reboot's runaway success and 150 million dollar budget the pressure to knock one out of the park every time will only get higher with each sequel. Any failure, dissapointment,or creative lapse will get magnified under such scrutiny.