This is what I did on my intros, following Jorats advice:
I introduced my girls in a neutral zone, aka the bath tub, with ONE of my boys at a time, starting with the most accepting of my boys, the alpha Gizmo. I did that with each one of my boys, one at a time for about 2 weeks. I did this with one boy at a time because Gyro had a history being aggressive to new rats, so I didn't want to take chances, despite he and the other boys are neutered, Nes had a bit of a rep too so I took it slow. At one point during the bathtub intros with Gyro, he got pretty puffy and hissed, whenever the girls got close. Soon as he did this I'd push the girls away or i'd move him away from the girls and stroke him, letting him know I was there to protect him like Jorats said.
After he calmed, 2 weeks later then I introed all the boys together with the girls for another week. After that went well, we stepped it up a bit more with the girls being in the playing zone of the boys. This was tedious because Nes and Gyro were very territorial for awhile. But then as if a flashlight turned on, the boys were all relaxed with the girls in their territory. So I put the girls in the main cage with the boys one night, and they were all getting along so well! I didn't plan on leaving the girls in there with the boys for the entire night, but you know what? It worked! They were all sleeping together! The slow and tedious with the intros paid off.
This was my intro story, its worked with me but i'm extra cautious because my boys had an aggressive rep with other rats. I'd say it neever hurts to be overly cautious.