The MIT license allows relicensing of the material and does not require that it be under the MIT license.
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
As described in What "sublicense" actually means? this means that you may incorporate your work and release it under a more restrictive license. In this case, removing the ability to sell copies of the software. That that with a significant grain of IANAL.
However, there's a bit 'gotcha' in this. The right to sell is part of the open source definition (and gnu philosophy).
The license must not restrict anyone from making use of the program in a specific field of endeavor. For example, it may not restrict the program from being used in a business, or from being used for genetic research.
As your modification would restrict a field of endeavor, it wouldn't be open source, nor compatible with other open source products which may lead to other difficulties.
But yes, you may relicense it anyway you want. The MIT is not a viral license and you can even take the entire project closed source if you so desire. But remember, that removing the right to sell is no longer free and open source. Your code could not be used in a GPL project, nor any other open source project with that restriction.