I have a very specific system when it comes to breeding
I house 1.4 rats and pull the pregnant females each week to put them in a birthing tub.
This way no back to back breeding
No fighting over babies which can lead to severe injuries/death
Once the babies are 10 days females go back in communal housing to raise their babies together.
Once weaned they go back in breeding rotation.
Works for me.
Now to the question can you leave the male in? Sure you can it's up to YOU to see what works for you and your colony.
Breeding takes trying things around I did and my method is what works for me.