haven't had my coffee so I may ramble on here.
If there has been no discussion of exclusivity or implied exclusivity you can continue to date other women.
If you are concerned about her being with other men, all I can say is be a better man than the other options, it doesn't mean spend more money, it doesn't mean have a bigger dick because no matter how much you're packing in either area there will always be someone packing more. Be the one that she thinks about when she goes to sleep the one she thinks about when she wakes up be her fantasy.
Capture her mind and her fantasies, explain her soul to her and she will be yours and no one can or will come inbetween you.
Bottom line is if you want to see other people because you are actually interested in other people then do it but if you are trying to date other people because of spite and your own ego can't handle the fact that she might be dating other guys then I think you have to look at yourself and become a mature man.
Really with women, give them the freedom to leave and chances are they'll stay and it displays that you are a confident man, women love confidence and she'll stay true to you if she doesn't then be a little sad and know that you are a good man and find another one who is a better fit for you.