^No it doesn't. That has never been established, but even if that had always been the case, you miss the thematic dissonance here. The swapping is a function, a device to get the two characters closer and see things from a perspective they couldn't. It's an excuse for them to kiss and rely on each other.
The moment you force in other girls to that equation you upset the balance and the point of the story. If you view swapping as a bond between two people, quite similar to a relationship, adding more partners means breaking that bond and having a third wheel. The other pairs that can swap have all become lovers, they have been loyal to each other only. Haruko and Natsuko have not reached that place yet. Natsuko in particular is always in denial. Unless the new swap partners are only there to reinforce that indeed, Natsuko likes Haruko, they are pointless and just muddle the idea.