Is the extras you pay at the moment something agreed on in writing or just a verbal understanding? For how long?
Could you be paying less? Possibly yes and still contributing to the costs you might think are worth contributing to. You can claim certain contributions as deductible of child support as long as you continue to pay at least 70% of your agreement amount I believe but you'd need to consult child support about this so the information could be relevant to your specific situation. And I think you would need to be paying directly to the school etc. This might mean you still end up paying more than the legally obligated child support amount though depending.
Legally, unless there is an agreement in place otherwise, you are only required to pay child support and that is it. What it is meant to cover isn't specified though, just the expense of raising a child in general so if a child is expected to coat more (specialist appointments, additional education costs etc) then that can be placed as an additional agreement.
Some do pay extra, my DD1s dad does contribute to I guess you could call it educational expenses (we homeschool) but it is flexible and discussed on a case by case basis. I'm not sure how things would change if he gets a new partner, we don't expect extra but it certainly helps improve the quality of the resources and experiences we provide so is helpful and appreciated but if he choose to stop we would not fight it. I think that can be a dangerous path for the co-parenting relationship and that is more important to me than the extra money.
I would suggest that your husband be the one to actually follow this up as it will probably be better received than if you do.