When a Type Certificate holder refuses to share the pre mod approval data and we own the design & certification data, could we apply for an EASA STC once the aircraft is with operator?

The ownership of the aircraft is not directly impacting considerations whether an individual aircraft can or cannot be modified through an EASA change. The fact that the Design Organisation must assess the interfaces of their change with the pre-mod configuration as applicable applies in general. In some cases there is no alternative to a commercial agreement  with the TC holder .