I kind of doubt that this is what you're looking for, but Melanie Rawn's Exiles of Ambrai series revolves in part around three sisters. However, one is definitely in opposition to the other two. It's a sprawling sci-fi/fantasy series and will probably be incomplete, as the long-promised third book has yet to be written (and book two ends on SUCH a cliffhanger, so it's quite a shame). The first book is The Ruins of Ambrai.

The other books I remember with a set of sisters are Dee Henderson's O'Malley series. Those are romantic fiction/crimesolving, albeit with a strong Christian orientation, so don't read if that's not your thing or you can't skip over it. However, while the family members are all definitely in each other's lives and show up frequently, each family member has his/her own book. I'd start with The Negotiator, although there is a prequel novel that doesn't directly deal with the main characters of the series.

Other than that, I can't think of too many sisters, which is a sad lack, although I do have several books with close female relationships, although they aren't the primary focus of the story (like Sharon Shinn's Mystic and Rider or Emma Bull's War for the Oaks).

I'll be watching this with interest to see what other people recommend!