Our only hard and fast rules are maintaining good communication, and keeping each other and any partners fully informed.
There is always a risk that a new relationship can supersede an existing one. We feel that if someone else truly does make us happier, then that relationship can/should become primary. In practice, our relationship (we are married) is so good that it difficult to imagine anyone else taking precedence, but we do realize it could happen. We would try to work with the circumstances if they arise. Now, if someone we are seeing tries to actively interfere with our existing relationship, they will be asked to stop - or to leave. Almost anything else is negotiable.
We have sometimes changed the frequency of seeing another partner or have rescheduled a date if one of us is experiencing a difficult time for any reason. Usually, talking about it is sufficient to resolve any issues, and a little flexibility in scheduling has taken care of any others.