No. The New York City Teaching Collaborative works with specific university partners which have agreed to support alternative certification teacher candidates. Partner Teachers are assigned to the university they will attend for graduate coursework based on their assigned subject area. Your certification area will dictate what university you will be assigned to. This means that universities ultimately decide what certification areas they are able to host.
To appeal a university assignment, Partner Teachers would have to appeal their subject area during the subject area appeal period. That period will be closed by the beginning of December 2023. Once the appeal window is closed, you cannot change your university for the duration of your degree.