There are lots of ways to do it
Many people who are in non-monogamous relationships that genuinely add to the quality of their relationship and life, only reap those rewards from a specific "style" of not being monogamous. Often what that translates to is that there are many many ways to approach alternative relationships that inevitably tick like time bombs and then blow up.
Maybe brainstorm with your partner some other ways to live your life the way you want to. Some people can only handle sex with others that is very casual. They tend to have a harder time with the emotional side of their partner's other relationships. If you are having problems it is a god idea to figure out what is the most problematic, the sex or the non-sex emotional aspect of the relationship with others.
Sometimes I think that the couples who have the easiest time (least problems) are the ones who do not have other relationships that are separate, maybe they see another person together because they have too hard of a time dealing with not being a part of the other relationship.
I kind of get the feeling that you are fishing for someone to point out that if you are indifferent about seeing others and she is adamant, just cross out the rule that says in order to be non-monogamous both of you must have other sexual relationships.
I always hated that rule,