My separation agreement states:
“From and after the execution of this Agreement, both parties shall live whole and separate and apart from each other, each free from the marital control and authority of the other to the same extent as though each were sole and unmarried. Each of said parties shall have the right to reside at such place or places and with such person or persons as he or she may desire or deem fit with respect to the minor child…In general, except for the rights and duties established by this Agreement, the parties shall hereinafter live as though the had never been married.”
Take that how you will…to me it sounds like you can have a relationship (sexual or not) with anyone you (or your spouse) pleases. It all depends on how your separation agreement is stated. You can both agree on provisions that can prevent each of you from being in a relationship or co-habitating with one of another sex.
Hope this helped!