You could simply allow two characters who haven't gone yet to swap their turns, assuming both are willing.
The description could be something like this. Imagine that the party needs to retreat. It's the fighter's turn, but the wizard is at the bottom of the order and the fighter is unwilling to leave him behind.
Joe suggests to Bob that their fighter and wizard characters swap turns. Bob agrees. "Seeing Bob's wizard hesitating, Joe's fighter grabs him by the arm and shoves him through the portal. Go! I'll keep them busy!" Bob gets to take his turn now (so his wizard can retreat) while Joe takes his turn on Bob's turn. Next round they return to their normal places in the turn order.
This is a great conversation! There are some pretty cool options out there that I hadn't considered. The reason that I suggested the 'take 10' was because this would be less complicated than delay. A character acts either on their initiative or on the 10 count. I would see this as for PCs only, the NPCs and monsters already have the advantage/disadvantage of being managed by a single mind.
PCs roll individual initiative. For the monsters, I break them into groups. So "Goblin Archers" get one roll, "Goblin Skirmishers" get their own roll, and the Goblin Leader gets his own roll. If a subgroup is particularly big (let's say there were 10 goblin skirmishers), I'll break them into group A and group B.
I also have house rule ready and delay rules that have not slowed down combat at all. But then again, I am a weirdo who finds combat to take about as long as it always has for my groups in whichever edition we played (and we played 2E with weapon speeds)
The one thing I do that aids in things is to not be completely dogmatic about the game mechanics when it comes to combat, and instead be more than willing to do narrative depending on what players/monsters wish to do.
Case in point, retreating. If the players want to retreat the game mechanics are set up such that the player moves, the monster moves and become adjacent, the player moves again and the monster gets an opportunity attack, the monster then move adjacent again, etc. etc. etc. And in "theory" the PC gets killed and can never get away if you stay strictly with game mechanic combat above all else.
Which is why I don't. If a PC runs off to retreat, I might have a monster move once to try and engage... but often I'll just zoom out narratively and say the monster watches the retreating PC, maybe fires a ranged attack at them if they have one, but otherwise the PC can just get away. And I can make that decision just as the DM for what makes sense to the narrative of the fight we are in, and thus never have to create these complex "house rule" systems for retreating in order to let PCs get away within the context of the game mechanics.
The game mechanics for combat are fine and all... but they aren't so great that I care to keep every single fight within their ruleset. At some point just waving my hand and saying "what makes story sense here?" trumps any need for an enslavement to the miniature combat rules.
Yeah tbh I’ll skip combat mechanics for a lot of stuff. The assassin wants to drop bear a mook? Okay. There’s no reason to roll init for that. Skill check to see how efficiently and quietly they can get it done, narrative, done.
One of the things I've been doing... probably since 2016... is that whenever two or more players have consecutive turns without any monster initiative between them, I not only let the players go in whatever order they'd like, but I also let them intermix their turns.
For ex, IF fighter, rogue, and wizard have initiatives 12, 10, and 6 with no monsters between them... the fighter and rogue could move, then wizard could take their turn to cast fireball, then fighter and rogue could move back to where they were (and attack if they still have actions left).
So far, haven't had any problems with it, and it seems to speed up play a bit (so long as I don't let the players get too hung up on "we need to choose who goes next").
Weird. I’ve done both individual and side-based for decades and never once has side-based go slower. About half the players typically race to go first. They have a plan and want to execute it. The other half have no idea what to do and flail while everyone else goes. By the time it’s their turn, they’ve figured it out and get on with it. The result being the players just go with minimal if any delays between them.
This basically reflects my experience, although I guess I assume that it's not that the "indecisive" half don't know what to do, it's that they want to see what actually succeeds to use that to inform their action.
Also, I kind of want the PCs to figure out how to work together. That's kind of what I like to have happen. Maybe it's rough sometimes where they have more than one conflicting idea. I let them figure it out. That's the game.
Honestly, the only drawback to side initiative is when one player wants to use it as a reason to bully the other players into doing what they want. I have had to stop and tell people that they're not a dictator -- even if their character is. However... I've had to do that with individual initiative, too.
I think my favorite house rule is to do a hybrid. Everyone rolls for initiative (the GM one roll for all monsters). Then the GM calls out, "Everyone above X, (where X = monster's turn) can go." Then GM goes. Then whoever is left. That allows some flexibility to the players, but only those who went faster than the monsters, and then those who went slower.