Yes, but playing your rivals more has at least two issues: 1) who decides what rivalries are selected and 2) possibly having some teams play much harder or much easier schedules than other teams.
Who would you have Maine play 3 times every season?
Based on 2016-17 league games
UML, BU, BC, PC, UVM, MC, NU, CT, UNH, ME, MA
Based on 2016-17 all games
UML, BU, PC, UVM, BC, NU, MC, CT, UNH, ME, MA
The top 2 and bottom 4 remain the same, but BC drops from 3 to 5 while PC and UVM both move up one spot each and MC and NU flip places.
Based on the last 5 seasons league games
BC, PC, UML, BU, UNH, NU, UVM, CT, MC, ME, MA
Base on the last 5 seasons all games
UML, BC, PC, BU, NU, UVM, UNH, MC, CT (3 yrs), ME, MA
Again, a fair amount of shifting, but the top 4 remain the same in 3 of the 4 cases, and 3 of the bottom 4 remain the same in all 4 cases.
I would try for a somewhat balanced schedule by ranking the teams using their 5 season overall winning percentage and then I would schedule 2 teams in the 5 top and 2 teams in the bottom 5 (excluding the team in question). For example, Maine is in 10th place my ranking above: They would play 3 games against 2 of UML, BC, PC, BU and NU and 3 games against 2 of UVM, UNH, MC, CT and MA. So, for example Maine could be scheduled to play 3 games against BC, BU, UNH and UVM.
I created a
possible 2016-17 schedule for Hockey East using my ranking which I put into a spreadsheet. Vermont was the 6th place team in my ranking so they are in the top 5 teams' top 5 and the bottom 5 teams' bottom 5.
Regarding more league games, I'm still working on league vs non-league attendance, but I now have 3 seasons (2014-17) averages and league games in general do have higher attendance.
Sean