While not technically impossible - the practical problem of finding SEVEN people who are all attracted (romantically/sexually) to each other at the same time...the odds seem vanishingly small. Finding THREE people who are interested in each other all to the same degree seems, from the stories here, to be a difficult enough endeavor.
Each additional person adds more and more complexity to the situation. You might want to check out the polymath
involved. Being all-bi or all-gay (either male or female) doesn't really diminish the complexity - not every gay male is attracted to every gay male, etc. (For instance, my boys are both straight and I am bi - we all are attracted to women. BUT not all of us are attracted to the SAME women, and even if we, somehow, were - that does NOT mean that she would be attracted to each of the three of US.)
Furthermore - attraction by itself is not enough to ensure a healthy functional relationship. Even LOVE is not enough...although many people delude themselves for years thinking that it SHOULD be.
This is an interesting thought experiment and could lead to an interesting idea for a novel...but in real life?