I understand that, generally speaking, you may not issue a license on a copyrighted work if you do not own the copyright to that work. Licensing is an exclusive right of the copyright holder. Instead, you may prepare a derivative your other people's work, and license your own changes under some license. Recipients of your derivative may then exercise whatever freedoms over the combined work that are permitted by both licenses.
However, the MIT license includes the right to "sublicense" the work, which suggests I may be able to offer the MIT-licensed work to others under different licensing terms. Is this correct?