While I don't think expansion beyond 32 is imminent, I do think we will see expansion to 36 or 40 in the not-too-distant future.

The idea would basically be to replace the first two rounds of best-of-seven with a six-team round robin. This would be best suited for leagues with four divisions, although 12 teams could be split into two groups by seed (one group would be 1, 4, 5, 8, 9, 12; the other would be 2, 3, 6, 7, 10, 11).

The six teams in each group (division) play a three-game series against each other with the higher seed hosting two of the three games. The team with the best record after 15 games advances to the conference finals. Alternatively, the third game in each series could not be played, and the team that wins the most series in each group or division advances. Either way, teams are guaranteed a minimum of five home games. Going by series wins could even allow a team that starts with an 0-5 record (assuming all five losses are to different teams) to come back and win all five series.

In the event of a tie in terms of series wins, one available tiebreak would be the team who required the fewest number of games to win either 3 or 4 series (if a team won all 5 series there will be no tie). Goal/point differential, fewest overtime wins, away wins, and head-to-head results against the tied teams could all be used as tiebreakers.

To prevent mathematically eliminated teams from mailing it in, draft picks could be awarded based on playoff results - i.e., a team that finishes third in its group drafts ahead of a team that finishes fourth. You can even still build a component of parity by having the all of the teams that finished third in their pool be ordered by regular season record, with the team that had the worst record amongst all third place finishers draft first among those four teams. For example, if the NHL's Panthers, Hurricanes, Avalanche, and Golden Knights all win their pools, the Panthers get the first pick among playoff teams (92 points in the regular season), followed by the Avalanche (109 points), Knights (111 points), and Hurricanes (113 points). All non-playoff teams would still draft ahead of the playoff teams, with the team with the worst record drafting first, subject to any lottery schemes implemented by their league.

The most attractive part of this is the relative efficiency compared to two rounds of best-of-seven. It at most requires teams to play 15 games, compared to a maximum of 14 now. It does have a higher minimum at 10 games versus 8, but it is not often that teams sweep 2 consecutive opponents. It guarantees five home games instead of four. It still incentivozes regular season performance as teams could have up to 10 home games.

This may require a bit of a paradigm shift in terms of TV, but the idea would be that each group plays its games at the same time every other day. To use the NHL as an example, the Atlantic and Central Divisions would play one night, and the Metropolitan and Pacific Divisions would play the next night, three times a week, for five weeks; weekend games could be scheduled over four to five TV windows instead of two. For weeknights, it may likely be a case of one being ESPN/TNT/FX and the other being something like ESPN2/TBS/truTV. It could also allow a third TV partner like Comcast (i.e. USA) or even the NBA and NHL Networks to carry live playoff games.