The NFL schedule is so very structured, so very precise, that it makes Monica from Friends look disorganized.
Adding an extra game wouldn't be a problem. Here is the current formula (I copied it from Wikipedia):
Each team plays twice against each of the other three teams in its division: once at home, and once on the road (six games).
Each team plays once against each of the four teams from another division within its own conference, with the assigned division based on a three-year rotation: two at home, and two on the road (four games).
Each team plays once against one team from each of the remaining two divisions within its conference, based on the final division standings from the prior season: one at home, one on the road (two games).
Each team plays once against each of the four teams from a division in the other conference, with the assigned division based on a four-year rotation: two at home, and two on the road (four games).
Adding an extra game should be no problem. First thing will be to figure out where the extra game comes from. It'll probably be based on your finishing position and against a team from the opposing conference. In other words, adding another game to #3 above.
This will be where the schedule nerds have to get creative figuring out a way to have the 32 teams alternating 9 home 8 road this year, 8 home 9 road next year.
They should be able to figure out a way to always alternate the two at home one on the road each year in a way that also fits the "1st place finisher in the NFC East plays the 2nd place finisher in the NFC West in years when the NFC East is on the NFC South (#2 above) cycle" rules. It could get little tricky, but I'm sure they'll have a big old math party to work it all out before they tell us how it will work.