Generally in the threesomes I have heard of, there was a couple who invited a third person to join them for sex. For the couple it is a way to have fun and to try new things, while sharing the experience. For the guest it is a way to have fun and to try new things. The point really isn't to develop the same intimacy with the third person that exists between the couple.

I have also met people who are polyamorous - meaning that they prefer to have intimate, romantic relationships with more than one person at a time. Each of these people said that even in relationships with multiple people, they would have one person they considered to be a primary partner. Though they shared intimacy with others, their connection with their primary partner was strongest. The people I spoke to didn't mention group activities, but I think it makes an interesting comparison.