It stands to reason that this is not possible. Because the license to implement the patent right is made by the patentee. Although it is licensed as an exclusive license, it is still not the patent owner and has no licensing rights. If a third party implements the patent, the patentee has the right to sue him. However, if you turn yourself into a patentee through patent transfer, you can license it to others. Exclusive license does not mean that you are the patent owner.