How about a temporary stacking resistance against the damage types?
If you get hit by thermal damage then for you get some extra resistance ( besides normal resistance ) against the next thermal damage. This resistance would gradually decrease with a set number per second. The amount of resistance would be based on the amount of damage taken compared to your maximum armor. Weapons firing at exactly the same time ( by pressing space ) only apply the resistance after all shots hit.
So for example a bot loses 10% hp from a thermal shot. After this it would gain a flat 25% decrease to the next thermal damage. This resistance would gradually decrease by say 10% per second. So if it was hit by another bot with the same strength thermal shot it would only lose 7,5% hp. This in turn would boost it's thermal resistance again by say 18,75% for a total of 43,75%.
The precise percentages would have to be changed but the end goal is that there will be diminishing returns for every extra bot firing at a target. So that 20 people wouldn't be twice as strong as 10 people, but only say 1,5 times as strong. The result would hopefully be that the extra coordination needed for an additional person would eventually outweigh the benefit of the damage they bring.
A big organised corp could still bring a large squad and with proper coordination and multiple target calling wreak havoc, but with lesser organisation you'd be limiting your effectiveness and thus giving smaller but more organised groups a chance.
It would also be a self-balancing mechanism if one race is stronger then the others. Each race does a majority of one damage type, so that damage type would be most used and thus the stacking resistances the highest. Thus other races would be more welcome in squads to add more variety to damage types. In the end the optimal group wouldn't be one with only the FotM race but instead one with a slight majority of FotM but still a decent representation of other races.
Lore/Physics wise the explanation would be simple. If your armor has been recently superheated by thermal damage then additional heating will have a reduced effect. If your armor and the underlying systems are already punctured by kinetic damage then additional kinetic damage will need to be much stronger to penetrate deep enough to hit the next row of internal systems. If your armor is already a compressed mess from seismic explosions then additional explosions will need more force to do an equal amount of damage. And adding more corrosive chemicals to an area that's already covered in them wouldn't do that much additional damage.