You're not supposed to pick a side if you want both to stay. There should be a third option telling you not to pick a side or something like that
According to the wiki, you need this:
Morgan is Kleio's ex! ![]()
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New in 20.2
Prerequisites: Done Hang with Kleio at the Mall, done Morgan cinema date, Location Pub, Kleio and Morgan present
Mike learns that Morgan and Kleio were together.
If you have 63 LP with both Morgan and Kleio, they each are 50 GP, and they each are >/= 25 KP then you can choose both of them. Otherwise, one or both of them will leave the game.