I found an article at RPIRatings.com that has a list of college basketball teams that have played each other 4 or more times in one season. It is not a comprehensive list, but it is still pretty impressive as it has data going back as far as 1906.
The article says:
Note that many of the teams in the following list are from the present-day Big 12 and Pac-10 conferences. Several of these teams had long travels to play games, especially before 1940, and it was common then to play a visiting team twice and then return the favor with a pair of games.
Based on their list (which includes the home, road, and neutral site records) it seems that up until the early 1970s, teams in certain conferences played each other 4 times during the conference's regular season. During that time, there were quite a few instances of 2 teams playing each other 5 or 6 times in one season, and one instance of 2 teams playing each other 7 times in one season.
But the article has a separate list of teams that have played each other at least 4 times in a season since 1975. I presume that since 1975, no conference has had their teams play each other 4 times during the regular season. Since 1975, there have been no teams that have played each other 5 times in one season.