Simple idea that could really shake things up and give ideas for team composition, bonuses for monsters being in the same team! These would proc at the start of battle and remain for the rest of the battle, despite monster deaths and revives (so no reprocing during a revive).
If you have a two monster bonus and the 3rd monster doesn't fit with the bonus, it'll still receive the bonus, meaning bonuses are team wide, not just the monsters proc'ing the bonus.

Examples are:
Llum the Magical Matriarch and General Ingvar:
-Diametrical Leaders +5000 Max HP/+10% Ability Accuracy

Ouros and Igursus and Cryotan:
-Monuments of the Ages +10k Max HP

Ouros and Igursus
-Fragments of Pandalf +300 Strength/+150 Speed

Igursus and Cryotan
-Fire and Ice +10% Accuracy/+2500 Max HP

Clivia and Alpha Cliviast
-Dark Forest Pollination +15% Lifesteal/+150 Speed

There are tons of potential bonuses that could be done, and could even have an extra little monsterpedia type thing that shows all potential bonuses and maybe even a little two sentence story explaining it, gives all the monsters a little more depth.

@Fox little tag for exposure sake.

@Zealot So are you thinking something like:
All in the family:
Violet, Galante, and Galante Jr. +10% ability accuracy

@Kaiju
Yes exactly stuff like that

@Zealot Something to keep in mind with rules like this is that it tends to favor people who have a LOT of monster power. I don't know about you, but it was probably a year of playing before I had all the monsters in the example, I just cited. If there were enough variations, it might even things, but early on in the game most players are trying to make sure they cover all the elements and all the books.

@Carlos some shameless plugging

@Clackers had I believe a similar idea with friendly monsters and unfriendly, hope i tell it right

I've thought on something like Marianne says. Monsters that work best together and worst if in the same team. I like this "chemistry" idea.

The easiest way of doing it would be to give a buff or debuff if they are friends or foes in the same team (stats-wise).

I like this, makes sense and has impact on game.

Noted

@Carlos said in Monster Team-up Bonuses!:

The easiest way of doing it would be to give a buff or debuff if they are friends or foes in the same team (stats-wise).

I like this idea, because at the moment having General Nishant and General Ingvar on the same team, while maybe nice doesn't make sense. Its like how in SWGOH you could have Jedi and Sith on the same side. Sorry no.

A General and his/her Nemesis in the same team should lead to a debuff I think, because they hate each other (expect Uria and Faraday, they hate Voltaik and Holter and Talos, because Holter doesn't even know about Talos )

@keki14 I can definitely dig the whole team debuff due to monsters hating each other.

@Carlos Be a little wary when doing that debuffing thing with Nemesises tho, especially when an entire team is composed of them. Some complaints are sure to emerge if the overall team is crap, despite the money spent