 If you liked
Haiyore! Nyaruko-san
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 ...then you might like
Kobayashi-san Chi no Maid Dragon
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Both shows have a main girl who decides to crash at a random stranger's house and forces them to take her in so she can grow romantically close to said stranger. A majority of the main cast are otherwordly beings( dragons and aliens ). They also feature many openly LGBT characters (but don't cross over into full yuri/yaoi territory),
If supernatural beings that arrive to the human world, have an instant crush on main character, and start a family life together is your thing; then these two shows might suffice your taste.
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