Here is a conceptual proposal for a way in which one could (partly) understand what “being together with someone else” means:

A is “together with” B ONLY IF:
A takes responsibility for her/his own life choices in front of B AND
B takes responsibility for her/his own life choices in front of A.

If: N is a necessary condition for P,
then: One cannot propose that P unless one proposes that N. (version: the proposal that P includes the proposal that N.)

So: Proposing that you “start being together” to someone else includes the proposal that both of you take responsibility for your own life choices in front of each other.

Note: Sincerity towards the other person with respect to all your life choices follows from this (you cannot be responsible in front of another person with respect to a life choice the other person knows nothing about).

Now: What distinguishes life choices from regular choices?

Here I do not think a conceptual analysis is required. When you know each other well you also know what the other person would consider a life choice. Also, instead of life choices one could speak of “what you’re doing with your life”. If one is unsure whether what one is doing counts for the other person as “doing something with one’s life”, one could always assume that it counts.

Side note: Naturally, this works for more than two people being together, too.

Methodological note: A proposed concept can be tested like any other artifact. A “beta tester” could just assume it and ask herself/himself:
– Does this concept accommodate my sense of being together with someone?
– Are there any intellectual troubles with respect to this particular relationship which could be alleviated by using this concept?
– Am I better guided in my actions (choosing to be together with someone or not, choosing what to do and what to refrain from doing when you are together with someone, etc.) by using this concept?
– Is there any overall improvement to my life as a result of conceiving being together with someone like this?
– Etc.