The center of this story is a facility known as 'The Baby Factory'. It is a place where men and women meet for safe, no strings, breeding. The usual practice is women pay to sign up for periods of time, between a few hours, a day, or for those who have the time and money, more than one consecutive day. They are given a private room with a bed, bathroom and a little more for comfort as they wait. A nude picture is taken as well.
Men come in throughout the day and night (open 24 hours), are shown a list of the pictures of each woman currently in a room and available. They then pay for a period of time, usually between a few minutes, a few hours, or possibly all night. The shorter times tend to be cheaper for men (very cheap for the few minutes), while longer times are cheaper for the women (giving more chance of a woman having several men if they want to). All customers are tested for STDs, but no other information is asked for. No names, ages (could be teen characters), marital status or anything like that. All payments are done in cash just to make it more anonymous. Though people can choose to talk about themselves in the room (including potentially contact information to meet again later), no one is required to reveal anything.
The women come for a variety of reasons, including but not limited too:
Maybe they work too much/have trouble getting close to people, and want to have one or more children without a relationship.
Maybe a lesbian who wants kids and for one reason or another, wants to do it the natural way.
A woman whose boyfriend/husband is impotent or never around and she is desperate for a child.
The woman’s parents keep bugging her about grandkids, and she decides to do it this way.
A few just want casual sex with strangers in a safer place and are willing to roll the dice on if they have a kid or not (or are turned on by the risk of it, and the fact the men are there to try to knock her up).
The men are often just happy to find a place where they can safely have casual sex without protection or consequences. Some are also there specifically to father children they will never see, because they either just don't want to deal with fatherhood or think they could not handle it, but still want to pass on their genes, possibly to numerous women.
It is focused on procreative sex, but no one is spying on the rooms, so nothing stops other varieties being occasionally mixed in.
There are a few ways this can be played. I could play one or more customers and you one or more of the women. I could play one of the women and you one or more of the men. Or I we could both play women who might interact during breaks between the men, while also playing the men for your woman (and if you are willing to play both genders we could both play women as well as the other woman's man/men). It is likely the women will need at least a few visits before impregnation. It is possible we could keep playing one or two women after successful conception.
In anything but the me playing woman, you playing man, I would prefer a female partner (nothing against guys playing girls, obviously, but think it can be more interesting with a woman's perspective in things like this).