I got this idea inspired by a lot of different MOBA's(It's not a game it's a genre-Multiplayer Online Battle Arena), so I think Pirate101's current 4v4 fits in well. In the MOBA genre every player typically picks one character(companion in this case) and use them to fight and in Wizard101 tournament there were special rules so...
For Pirate101 I got this idea, a 4v4 elimination(Defeat All Enemies) pvp where every pirate only choose ONE companion(Your character,pet are banned). In the start all player will get a minute to ban a companion, everyone take turns.(Companion that are banned are unusable by ANY pirate on both teams, if the "banner" decided to not choose to ban a companion of the time runs out no companion will be banned for that turn, so in average 8 companions will be banned from being used if every pirate/player bans one),also if that companion have a crown shop counter part and its questing counter part is banned the "counterpart" is also banned.
The banning turn should go like this Red Team's 1(First Player) bans first, then Blue Team's 1 bans, then RT's 2(second player) bans,then BT's 2 bans,RT's 3 bans, BT's 3 bans...and so one(which teams ban first will be random).
After the banning phase, everyone takes turn choosing a companion(Everyone gets 30 seconds, if no companion were chosen then the firstmate, if the firstmate is banned then their "secondmate" if it also banned then the "thirdmate" and so on), note: EVERY SINGLE PLAYER MUST CHOOSE A DIFFERENT COMPANION(so if someone took Bonnie you cannot choose her),everyone takes turn choosing a companion just like the "banning phase" so your selection will be revealed to both your allies and you opponents(Pros and cons for choosing early- Pro:You get the dibs in the companion selection, Con: Your enemeys might try to counter it). So who choose first?- The team who gone second will get to choose first so here the routine-2nd Team 1 go first then,1nd Team 1 goes,2nd Team 2 chooses,1 Team 2 selects...and again so on.
The rest of the PvP battle process goes like normal(the current on who moves first and do what, the battle board size should maintain the same, and where the companion starts in the PvP should be like your typical 4v4 so no one can take advantage of those AOE Buffs and AOE unlimited range attacks that easily.
This in my opinion should give a new play style and strategies for PvP while trying to predict what companion your opponent gonna use from a long list of them. I think this should be done by Maxed levels with at least 16 well trained companions(This should motivate them to train them more), or even by low levels(though maybe removing a few bans or allow repetitive companions be used).

Yours sincerely,
Angel