Personally, I've been brainstorming a race of haplo-diploidal eusocial mammalian-like humanoid aliens who, biologically, would be divided among the following 3 classes based on sex chromosome count (with cultural titles inspired by feudal European castes):
Single X chromosome: Serfs, infertile workers with a child-like intelligence, whose main purpose is to support the noble mother that gave birth to them, along with the colony that they, along with their mother and siblings, including other nobles that their mother might've given birth to, live and dwell within (which would likely be about the size of a small village of a hundred or so members). However, despite their low intelligence, and their instinctual imperative to keep their colony alive and reproducing, even the serfs within the colony are quite capable of independent thought and talent, and with it, are quite capable of performing not just dumb labor (including tending to their younger siblings like babysitters or nannies), but also skilled, and even creative, labor tasks, much like the ones found within human civilization, from farmers, carpenters, and electricians, to soldiers, and even scientists!
XY chromosome pair: Princes, male drones whose sole purpose is to inseminate whatever female nobles are nearby (especially those nobles whom haven't been inseminated by a prince as of yet), with at least one of these nobles being chosen by the prince (usually, though not necessarily always) to become a princess that's capable of bearing their sons through continuous intercourse (to stimulate their noble mate's growth into a form that would allow their male princely offspring to properly gestate without being aborted via miscarriage). A prince who has fathered many princes and princesses is often referred to as a king, and often possesses widespread social influence comparable to one.
XX chromosome pair: Collectively called nobles or ladies (with different sub-classes according to physiological development), they're akin to insect hive queens, though unlike them, while all nobles (with a few rare exceptions) are able to lay eggs that hatch into serfs (without requiring sexual intercourse, a.k.a. asexual reproduction), not all of these nobles are able to give birth to other nobles, and only a select few are able to give birth to princes (though all nobles have the potential to give birth to both nobles and princes, albeit a potential that can only be awakened depending on how often they've had intercourse with a prince). All nobles possess two wombs, one that's designed to continuously gestate the eggs that the nobles lay, which then hatch into serfs, and another womb, where egg cells are waiting to be fertilized by a prince's sperm in order to turn into zygotes that gradually transform into infant nobles or princes, which gestate at a slower rate, and are born live (like mammals and humans).
The noble class could be sub-divided into the following sub-classes:
--- Maidens: Taskmaster-like nobles who can only give birth to serfs, and can only morph into the next sub-caste by being inseminated by a drone. (Even once will do, since the drone's sperm would then be carried and preserved within one of the noble's 2 wombs.) They typically watch over the serfs that they give birth to, much like the mother of a household, and also often socialize with other nobles, especially their parents and siblings.
--- Mistresses: Insemination by a drone triggers a hormonal reaction within a maiden's body that not only supplies her with semen, but also gradually transforms her into a mistress, a minister-like noble that, in addition to laying eggs that hatch into serfs, gains the ability to give birth to infant maidens, though still lacks the ability to gestate princes (which requires constant intercourse from the prince). In addition to managing the serfs that they give birth to, they also watch over the nobles that they've given birth to, and even socialize with other nobles within a "court", a group of nobles that are centered around the prince that inseminated and fertilized them. Oftentimes, they'd watch over several nearby villages like a countess.
--- Princesses: Regular insemination by a prince would provide a mistress the ability to sustain the gestation and birth of infant princes to further spread both the prince's and noble's genes far and wide for generations to come. By then, the mistress would be considered a princess, despite the physiological changes between the two noble sub-classes being so subtle. (In fact, a princess could revert back into a mistress if their prince no longer engages in frequent intercourse with them, such as if the prince had died, or if the prince had wanted to spend more time with another noble.) Like with other nobles, these princesses would typically attempt to remain in touch with their offspring, siblings, and parents (including their prince's parents), though given how their numerous princely sons tend to flock to lands far and wide in search of nobles to mate with, they might also end up watching over vast lands, with about as much influence as the queen of a monarchy. In fact, a princess that has mothered many princes and princesses is often referred to as a queen, with widespread social influence comparable to one.
Now there may be implications towards my eusocial species' traits (such as the possibility that nearly every noble might be made into a princess if there are equal numbers of princes, resulting in a society that would mirror our modern-day monogamous society, with each prince and princess paired with eachother like husband and wife), but enough about my eusocial race's epic physiological, behavioral, and cultural lorecrafting.
One thing I'd recommend keeping in mind when designing a sentient race with large family sizes is Dunbar's Number. That is, whereas the average human can handle being within a social group that's 150 members large, you ought to ask yourself this: "How big of a social group can each member of each caste handle within their own social groups?" For my eusocial race, I'm personally going with around 150 members each, regardless of caste, so that I'd then have a system where each serf, noble, and prince would only be capable of meaningfully socializing with their immediate family members, including parents, children, siblings, and in some cases, in-laws, since they'd all likely add up to numbers that might stress their social capacity to the limit, with each member of their social group occupying various ranks within a much broader social and familial hierarchy, from the lowliest serf to potentially (though rarely) the queen and king of a vast family tree.
How the queens of your eusocial race would socially be able to handle laying around 3 million eggs per day, let alone interacting with their entourages of around 6,000 protectors, will ultimately be up to you to determine.