Most people remove the male before the babies are born. The female will get pregnant again instantly. I like to let her rest up a bit. I have two males that I use for breeding and then put them back together again. I didn't even know you couldn't do this. They seem to get along fine!
I agree, I actually have a rat birthing rack. Each prego female gets her own tub to give birth in. I leave her in her tub until she weans her babies, then she goes back into breeding circulation.