I had a borderline mucinous tumor removed last year. I was staged at the time of the first surgery. After they found it had borderline I had a complete hysterectomy done a few months later as I also had a history of high grade pre-cancerous changes in my cervix. Luckily I had 2 children already but I was only 32. I'm now in the unfortunate position of having my tumor recur in my bowel and require more extensive surgery. My tumor had ruptured prior to surgery so I think that put me at higher risk.
Some doctor like to make out a borderline tumor is nothing to worry about but they can and do recur. My doctor also recommends 3 monthly checks with a ca 125 blood test.
You may not need further surgery to stage. It seems they already know it was a serous borderline tumor, which is most of the information needed to decide on treatment. Typically, chemo is not given for this type of borderline cancer. You will most likely need to go for check-ups every 3 months.
I had a serous borderline tumor over 2 years ago. I was staged during surgery only because my surgery was done by a gynoc (they suspected cancer from the outset). I was staged 1C, but no chemo was needed. I went every 3 months for check-ups for a while and now I go every 6 months.
This type of tumor doesn't usually recur, and if it does, more surgery is the treatment.
Hope this helps!