You won’t be able to keep all your stats, (because that would make the game stop 1) making sense and 2) working as intended)
For every background you successfully beat the game with, you will get (the option of?) starting stat bonuses (These won’t be huge, but will help.) You get more for however many backgrounds you beat, but you only get the bonus once.
Two stats will get +5. 
Assuming you manage to meet their requirements during your first playthrough/a complete playthrough you will unlock 3 new backgrounds. Each of which include a lot more information on things that you can only guess at during non-bonus background playthroughs
Same as above, assuming you unlock them, there are 3 new romance characters to unlock, each of which while not being involved in the main story will have major stories of their own, romancing them will let you know a lot of things that are going on behind the scenes/below the surface of the Summit
On top of the fact that new playthroughs will give you a chance to see different content that you didn’t get to see the first time.
It’s literally impossible to see anywhere near all the content in one playthrough. To see it all you will have to play all the backgrounds, romance all the characters and make sure those characters do all the different possible things and have all the different personalities between them.
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