I would look at some of the room sharing threads on here regarding blended families.
For me the biggest consideration would be, do you live in a five bedroom house?
You don't say what sex your children are but there is already quite a significant age gap between your two and it's not clear whether your youngest who is the same age as your partner's child is a boy or a girl. You should consider and allow for the possibility that your partner's son might at some point need to come and live with you full time.
I would say that unless you have enough space for each of your children, including a potential new baby, and your partner's son when he comes to stay, to have their own room, having another baby is more about what the adults in this situation want than about the needs of the children who already exist.
A lot of people will no doubt come along and say nobody ever died from having to share a room as a child, but just look at some of those threads and you will see what I mean.
There was one recently where the OP's 12 year old daughter and 16 year old stepson had been forced to share a room until the OP's 20 year old autistic son moved out, each of them had finally got their own space, then the 20 year old autistic son moved back home and wanted his room back. It turned into a bitter row with some people saying the 20 year old son should be chucked out because his needs had been prioritised over those of the other children for far too long, and others, who I suspect have autistic children themselves, saying that his needs are paramount regardless of his age and that the 16 year old stepson should be kicked out and sent to live with his mother.
There have been various others where, for example, there has been a heated debate over whether a bedroom should be given to a new baby or whether the baby should share with a much older sibling of the same sex so that a step sibling of the opposite sex could have their own room when they came to stay.
Have a read of some of those threads and ask yourself, "Could this be us if we have another baby?" If the answer is yes, don't have another baby.