The answer is: It depends. The norms around whether the results from a single study can be written up in more than one thesis or dissertation vary by university, field, lab, country, advisor, and thesis committee. There are some places where it is explicitly forbidden. In other places, it is common in at least some form. At my graduate school (MIT), collaborative PhDs are rare but possible.
It cases where it is possible, however, it is up to the thesis supervisor, the thesis committee, the department committee, and the university to ensure that each thesis reflects the work of each thesis author — in both quality and quantity of work done by that individual — to justify the degree being conferred. Sometimes, this means that each thesis must describe a sub-part of the work that each author was the intellectual lead of. Sometimes, this means that each thesis describe a separate extension of the shared work. Sometimes, it means a single thesis with two degrees. Sometimes, it means that it's simply not possible. Figuring this out is subjective.
The only things that always true is (a) that it must be both explicitly documented and well explained both that the thesis contains joint work and what each author contributed, and (b) that everyone involved must be supportive of going forward with multiple degrees reflecting a single body of work.
In your situation, it sounds like your supervisor believes that this is not the case. Why does your supervisor think it's not appropriate in your case? You'll just have to ask them.