Rats (superfamily Muroidea) have a well-studied mating system that often involves males becoming sexually satiated.

This means that they literally get tapped out of sperm and it takes approximately fifteen days for their fertility to be completely restored.
Various ejaculate parameters recover slowly, including components of seminal plugs and the semen itself.
Interestingly, male rats exhibit something called the Coolidge effect, whereby exposure to a novel female stimulates sexual behaviour, even in sexually satiated males.
So despite the fact he’s got no semen to deposit into novel females, the male will go ahead and copulate with them anyway because it’s still possible for him to mount and insert his penis into a female’s vagina.
He just doesn’t ejaculate.

Now, why would males engage in such behaviour when it’s energetically wasteful and he has no chance of siring any offspring?
He does this in order to remove mating plugs that were deposited by previous copulatory partners.
It’s been found experimentally that these “non-seminal” copulations actually function to dislodge the mating plug and thereby remove competitors’ sperm.
This post is an adapted excerpt from my book “Wild Sex: The Science Behind Mating in the Animal Kingdom“