I don't see why it would, the bonus from multiple charismatic pops and the Xenophile bonus have no cap.
Honestly, because the only way to make Domestic Servitude really pay off as an investment is to give it a significant happiness boost. If we assume the bare minimum of 1% per domestic, then gene mod that race to be charismatic because it's what they're for so might as well. It would still be 2% happiness for tile dedicated to that purpose. 2 happiness translates to a .8% increase in every other tile. You'd have to be running over a 100 tiles for that individual bonus to be worth more to you than just another mine, or another lab.
But Domestic Servants don't just add happiness. That tile is also producing, lets say we dropped it on a +2 food tile, 10 food, it's helping combat unrest, and adding xenophobic population attraction which is probably a positive for you if you're running Domestic Servants.
I suggest those positives don't counter act the drawbacks AND don't justify the micromanagement labor and influence cost it's going to take to plant a slave race of domestic servants on your planet. Even if you have to farm anyway, by opting to use Domestic Servants instead of Chattel Slaves, you are giving up a 20% efficiency bonus to their output. Spaced out over enough slaves to feed your empire, that is a huge food loss or a large number of tile wastes.
So, I jump ahead in the numbers tweaking process and conclude it won't be a bare minimum 1% bonus. It'll be higher than that, how high do you need to make it for it to be significant? Well, pulling a number out of the air, a 5% happiness bonus would translate to an overall increase of production on the other tiles of 2% That gives you a break even point at 50 tiles, any planet with less than 50 tiles suffers a loss of efficiency at 5% happiness. If you add Charismatic to that for 6% happiness bonus it becomes 2.4% overall increase for the other tiles and that gets you a break even point at 42 Tiles.
Now you're obviously crunching the numbers in your head and you've determined that even 5% happiness is a hard sell for being worthwhile on just the strength of resource collection. First no planet has 42 tiles much less 50 so on the numbers alone this falls behind. It gets worse when you compare it to the agrarian world strategy of dedicating a single world to mass producing food. Creating an agrarian world doesn't require the micromanagement of population transferring, it comes with the flat influence cost of colonizing, it produces more food overall which means it clears up more tiles for important jobs. And on those planets with their food tiles freed up, you also get a greater advantage for bonuses to whatever specialty they do happen to have. Even at 5% happiness, this is not an optimum strategy.
Here's why I'm still saying 5% happiness. At 5% happiness, 6% after a gene modification project, you have the effect of a Monument of Purity just by conquering an alien race, transporting two slaves to your planet, and placing them on 2 farms. This will affect unrest, this will make your planet more stable, if you allow free migration this may convince your people to stay home. This may even refund you the cost of building a Monument of Purity which starts to look like a wasted tile. 5% won't be optimal, but in extreme numbers it may render certain problems insignificant.
So I guess I'm asking if there's a cap because I'm assuming they're going to make the happiness bonus significant from a resource standpoint, and so believe that they'll have to institute a cap to prevent it from being game altering in other ways.
The exact mechanics of how domestic servants affect happiness is something I would really like to know. My first game come Utopia is going to be authoritarian but not materialist. Part of my plan (if possible) is to set robots as domestic servants and build one or two on my energy and science specialized planets.
Currently you can't enslave Robots or Droids, only Synthetics, and I don't see anything about the upcoming expansion that will change that.
