You can just change the license, that's what MIT allows for. You are allowed to do whatever you want:

  MIT License

  Copyright (c) [year] [fullname]

  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), **to deal
  in the Software without restriction**, including **without limitation** the rights
  to use, copy, *modify*, merge, publish, distribute, *sublicense*, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:

  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.

  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.

You have to keep the copyright notice and notice of existing permissions, but that is not the same thing as a license. And you are allowed to sublicense into a more restrictive license (such as proprietary/closed source). Just not the other way around, which is what the inclusion of the existing notice helps to enforce.