There are some leagues that toy with something like this, though I'm not sure if any go to both a group stage and then follow it with knock out rounds.
Here's the summary from Wikipedia (standard disclaimers apply, though this squares with my memory) as to how Belgium works. They put the top 6 teams in a round robin. Rather than rewarding placement during the regular season with home-away imbalance, they start each team with 50% of the points they got during the regular season so the top teams get an advantage, but perhaps not an insurmountable advantage. It would be interesting to back test to see how the results of the Championship Playoff compared to the result of the Regular season. I love the excitement of playoffs, but hate the lack of correlation in MLS between regular season performance and playoff outcomes, particularly since MLS Cup is considered the ultimate prize.
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Regular season[edit]
Each of the 16 competitors in the Pro League hosts every other team once in the regular season, for a total of 30 matches between July and March. A win earns three points and a draw earns one point. Teams are ranked by total points, then by total wins and finally by goal difference, number of scored goals, number of away goals and number of away wins. If teams are still level, a test-match is played in two legs to determine the final order in the standings. A playoff phase is then played from March to May.
Championship Playoff[edit]
The point system in the championship playoff is the same as during the regular season, except that each team starts with half of the points they won in the regular season, rounded up to the nearest integer. The points gained by rounding are deducted in the case of a tie.
The top 6 teams from the regular season enter the championship playoff, with the first-placed team winning the championship of Belgium. Each team plays their opponents twice, and the teams are ranked by points, points from rounding, wins, etc. as in the regular season.