The Big Ten did that in 1981 and 1982.
Everybody played 9 games except for Iowa and Ohio St. Of course Iowa and Ohio St tied for first with 6-2 records and Iowa and Ohio St did not play each other. Iowa ended up going to the Rose Bowl because the 3rd tiebreaker was who had gone the longest since their last Rose Bowl.
In 1983 and 1984 the Big Ten went with a full round robin 9-game schedule. Illinois went 9-0 in 1983 and is the only team in Big Ten history to beat every team in the conference.
In 1985 the Big Ten went back to 8 games, which lasted until 2016, when the Big Ten started playing 9 games.