I’m guessing he wants to take over, people view him as a God/king who’s all saint and to get Medea as his wife. Since she is fit to be with him because she has been taught how to do things.
Eros has always had what he wants since he was a child. Being the king doesn't interest him in the slightest. What he wants is Physche's divine healing ability so that he can not only be the ruler of the empire but a god amongst regular humans. That way, no one can ever get in his way. Thats why he used that sacred relic as a necklace (extracts divine power. So it would steal physches power and then he could take it) on Physche in the chapter where Medea almost died in Physches body. He took a slight interest in Medea because unlike everyone else, he noticed that she sees him as a tool for her to raise her own title (princess/his fiance). So he thinks Medea is more interesting/entertaining than all the other boring humans.
So that is why. It's always the greed that makes everyone do things. I actually like his character more than medea's father.
Can someone tell me what Eros goal is ?