My son's mother (29F) keeps having children with no father and expects me (29M) to take care of them?

I (29M) have a son (10) with my ex (29F). We broke up when she was pregnant and she wasn't sure if my son was my child or not. A DNA test proved paternity and I have been an involved dad ever since. We shared physical and legal custody of our son and parenting time is 7-7.

My ex has four more children and is currently expecting her fifth. None of her children have the same father. Other than my son none of the father's are involved in any capacity. She gets no help with the other children at all and for years she has been asking me to pick up the slack. When she had her second I refused and I told her she needed to find someone else to play the role of a surrogate dad to her other child. But she made the same choices each time and has learned nothing.

It has made her unstable and my son hates living with his mom. They don't have a lot and there's always tension and other issues going on at her house but the courts do not want to change the custody schedule. My ex has even told our son it's my fault her house is the way it is and my son saw a therapist who attested to this in court. It wasn't enough. So until my son is older (16) this is the way custody will be.

I have tried to be kind when turning down my ex so our relationship as co-parents isn't poisoned even more. But that is proving to be increasingly difficult as she adds more kids and begs me to do something. I would resent doing it. I only have one child and who knows how many she will end up having. To expect me to be a fatherly figure or even a family member who helps financially all of them is asking for too much. It would make me incredibly incredibly resentful.

For those wondering what exactly has been asked of me: To include all the kids in outings and I pay, to buy Birthday/Christmas gifts for all the kids and make sure they all have the same, to buy clothes and school supplies for the other kids, to spend time with the other kids, to pay more child support so that it can be used on all of the children.

I'm here because I know none of this is good for my son but my hands are tied. He is who I care about most of all. He is my responsibility. Not his half siblings or his mom. And I don't even know if I can do more than I have.