I've run into a few people whose take on "non-monogamy" in any of its forms translates loosely as "staying with your current partner until you find something better". Unfortunately, there is some basis for this in reality. Some people DO stay in one relationship until they have a new one to replace it because they do not want to be "between relationships".
This may or may not be what your partner is doing, but you should probably sit down together, each make a list of your hopes and fears (even the outrageous, irrational ones), share your lists with each other, and see how different or alike your lists are. If you can verbally reassure each other on most of the key items, you will probably be ok. If not, you may want to re-evaluate how fundamentally compatible you are over the long-term.
Some people are "poly" or "mono" all their lives and know of no other way to be. Others are "mono" at first until they discover that "poly" is an option. Still others "experiment" with "poly" in their younger years, then "grow out of it" and "settle down". I think sometimes the "mono" partner of a "poly" person might hope that it is the last thing - they think they if they let the "poly" partner "get it out of their system", the "poly" partner will "come around" and eventually "be normal".
I put all those things in quotes because they are labels and generalizations, and there are other words that could be used to describe the same concepts. Essentially, you should figure out which one you are and which one your boyfriend is, and take things from there. Easier said than done - I realize people usually want what they already have to work out, but if you break up you can always get back together if it turns out to be the wrong decision.