NRE is a powerful thing, and when it is in a poly context, can cause a hole mess of emotions. But it can be learned how to enjoy it and bathe in it while still holding on to the other things that you value (i.e. your existing relationships). I was horribly bad at getting totally consumed with NRE - or "the shiny", as I called it. Now I take time to stop and think about what I care about, and I make sure I get feedback from my existing partner.
See, the problem is that, especially in the early experiences of poly, that initial period with a new lover is the ab solute toughest time for your existing partner. Fears of abandonment, jealousy, envy and a whole bunch of other emotions can rage, which is a huge downer on the couple experiencing the NRE.
It is absolutely vital, in my opinion, that the person (or persons) that are having the NRE and in an existing relationship be responsible, take a step back, and make sure that everything else is fine, without totally immersing themselves in the NRE to the exclusion of everything else.
Finding a balance is the key part, and that point is going to differ with different people, according to their own experiences and backgrounds.
"Listen, or your tongue will make you deaf." - Native American Proverb