Two primary things make transitioning from mono- to poly- much easier while in a couple.
The first is having a solid enough loving relationship with good enough communication (I threw in the 'enough') because we're all human and few of us have the ideal or perfect in these dimensions.
The second thing which helps tremendously is for both partners in the couple to practice, regularly, examining their unconsciously held and unexamined beliefs about love and sex and family and all of that. If one believes, somewhere in their psyche, that only monogamous couples can and do "really" or "fully" love one another, one is obviously going to experience fear of loss of love in transitioning to poly-. Bringing the many very specific beliefs about love and relationships we've been living in accord with into conscious awareness and asking "But is that true?" about each of them is a powerfully transformative practice, especially when one is willing to do this with serious engagement and radical self-honesty.
There are quite a number of primary beliefs which most people in our culture subscribe to which are flat out false. Learn how to test them for truth and falsity. Belief example: "If I have two lovers I must have only half as much love to give to each as if I had only one lover." (... and a third as much if I have three lovers.) Learn to see what sorts of metaphors or analogies are at play. In this case, the analogy is false, thus rendering the whole premise false. The analogy here is to pie, cake, pizza.... It is true with pie, cake, and pizza that if I share a pie with three others fairly I must divide it into fourths--that is, if everyone wants an equal proportion.
When we think of love as a commodity or substance which is limited in supply, like a pie, we fundamentally misunderstand the power of love to expand when given -- quite the opposite of the behavior of pie. We also fail to take into account the success stories of polyamorous people who often report having their love grow for their first (chronologically) love while opening to another lover as well.
It is true that time is like pie in that it isn't unlimited in supply. If you work a busy week and most of your available "free time" is on weekends or vacations, that's quantifiable and limited. Sadly. But a loving person with two lovers will naturally do her/his best to spend plenty of quality time with his/her lovers.
I suppose the basic essence of this second item on my list of things we can do to smooth our transition to poly- from mono- is about subjecting our cultural conditioning and indoctrination--which is lodged in our emotions without our knowledge or consent--to self-honest rational inquiry. That's always a good thing to do with beliefs of the present-but-unexamined sort.