There was a movie I saw about 6 years ago. I think it involved 3 sisters, but you weren't really aware they were sisters. It seemed to be about three different people and their stories, then towards the end of the movie, they all come together and you become aware of their relationships. I think it was a story about connectedness.

I know of one movie in particular about three sisters...

Hanging Up (2000)

With lisa kudrow, meg ryan, and diane keaton

Oh, but they knew they were sisters.

I think your thinking of Playing by Heart. It came out in 1998. Angelina Jolie and Gillian Anderson were two of the three sisters. The sisters' boyfriends were Jon Stewart, Ryan Phillipe and Dennis Quaid. Their father was played by Sean Connery.

They all come together at the end for the parents' anniversary party.