Six sisters are competing to win the affection of boy for most

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Six sisters are competing to win the affection of boy for most of their school life. The boy is pure hearted and blissfully unaware of why his six friends are so pushy and touchy with him. All the sisters are some kind of -dere archetype. One day, a new girl arrives who does not conform to any dere archetype. She is a genuinely nice person, and the MC develops a crush on her and asks his six friends for help in pursuing her. Because they can't say no to anything the boy asks, the six sisters agree to help like morons.
With time to highschool graduation ticking down day by day, the six sisters realize they must set aside their differences and that they must make a pact if they don't want to lose the boy. They must keep the boy and the new girl away from each other at all costs, and then agree to share him at the end. Or at least that's what they have on paper...