I think that only happens if the question word refers to the subject of the sentence and that is plural or a list. In this case the bosses are the object.
Does "What type of bosses do you know?" work as well? I feel like there might be a subtle difference, but "what type" is always what comes to mind when I see "milyen" instead of "what kind".
"Milyen" is a question refers to quality. Red, tall, boring, ... What kind, What type are similar meaning. "milyen", "miféle", "milyen fajta" -> "what kind" - "milyen típusú" -> "what type"
In past lessons "milyen" was translated as "what is......like". So why can't this sentence be translated as: "Do you know what bosses are like?" If it can't, then how would you say that in hungarian?
Another translation would be "What are the bosses that you know like?", so it fits your pattern, however the question word refers to the type/quality of the bosses you know and the fact of knowing some bosses and also knowing what they are like is not questioned. "Do you know what bosses are like?" would be translated as "Tudod milyenek a főnökök?" or a little bit unnatural but still correct using the same word as this sentence would be "Ismered milyenek a főnökök?".
Tak jak po polsku używasz zaimka "jaki": "Jacy są szefowie?" - "Milyenek fonokok?" albo "Jakich szefów lubisz?" - "Milyen fonokoket ismersz".
what about this: "Which bosses do you know?" Could that be a legitimate answer?
"Milyen" asks for qualities or types. "Which" would be translated as "melyik" and asks for particular people. "Melyik főnököket ismered?" - "Which bosses do you know?"