I've been checking out Star Wars - Edge of the Empire and I really like the initiative system used in it.
... Once all Initiative checks have been made, the CM notes down the results of each check and ranks them in order, from highest number of successes to lowest number of successes.
STEP 2: ASSIGN INITIATIVE SLOTS
Once the GM has determined the Initiative order, he notes which results were generated by Player Characters, and which results were generated by NPCs. The results generated by Player Characters become Player Character Initiative slots. The results generated by NPCs become NPC Initiative slots.
STEP 3: PARTICIPANTS TAKE TURNS
Beginning at the top of the Initiative order, the players and CM fill each Initiative slot one at a time with a character turn. If the Initiative slot is a Player Character Initiative slot, then the players agree on one Player Character to fill the slot from amongst the Player Characters who have not acted that round. That Player Character then takes this turn. If the Initiative slot is an NPC Initiative slot, then the CM chooses one NPC to fill the slot from amongst the NPCs who have not acted that round. That NPC then takes this turn.
In essence, players roll initiative 'slots' that can then be used by any player to take their turns each round.
I'm considering implementing this in my 5e campaign, as I'm not a huge fan of the static initiative rules they currently have. Players would roll for initiative as normal, but then would be able to freely choose their turn order within the rolled slots.
I realize this would be a significant step up in power for the PCs, as they would be able to much more consistently pull off synergies between classes that are highly dependent on turn order (eg. barbarian knocks enemy prone and rogue can get the sneak attack before the enemy stands back up), as well as increasing the potential effects of 'until end of next turn' features (eg. monk going first on round 1, using stunning strike, then going last on turn 2 so the enemy is effectively stunned for 2 rounds). However, I plan to combat this by having enemies able to use the same system to gain similar advantages.
My aim is to enable tactical choices regarding turn order and initiative, beyond those of the base rules.
Considering the above, to what extent would using this initiative system break/unbalance the game? I'm fine with an overall increase in power level, as I can adjust encounters etc. to suit but I'd like to avoid upsetting the class balance if possible.