Just looking at the way our fixtures fall, I reckon Cooky could be available for 5 of those 8 matches.
Certainly the next two and I reckon the last three, as the first day (12th September) of those is the day after the final test against the Windies.
They definitely won't let him play the day after the last test. Those days are long gone.
They may not even let him play any of the final three. He won't have had a break since February and whilst he could probably play an extra month England will be looking ahead to an Ashes tour November-January and then NZ in February/March. If we work backwards from the first warm-up game 4th November in Perth, England will probably look to fly end of October. They'll need to prepare prior to flying out. Let's say a month (as that is how long a county team would generally take to prepare for a new season) to prepare - working on fitness, fielding and netting and maybe some team building with a training camp in Spain. That takes us to end of September. If Cook's going to have a break/holiday between February 2017 and February 2018 it's therefore likely to have to be the second half of September. Maybe they let him play the penultimate round of matches but it's probably easier to just shut him down entirely after the final test.