I'm making some modifications to this project licensed under MIT License.
The thing is: I don't know what to do to their license file. Do I just override with my stuff?!
You must never remove existing legal notices. However, if your modifications are more than trivial changes, you can add your own copyright notice to the existing notice.
For example, if this is the current license notice:
Copyright 2011-2018 Original Author Permission is hereby granted ... [MIT License]
You could add your own notice above:
Copyright 2019 João Lucas Copyright 2011-2018 Original Author Permission is hereby granted ... [MIT License]
However, this is somewhat unusual. Many projects only list a project founder in their copyright notice, but not all contributors that also hold a part of the copyright. Since copyright is automatic and does not require such notices this won't affect your rights either way.
The MIT license only requires that its notice is preserved, but does not require that you make your modifications available under the same license. Though doing this is unusual, it is your right to choose any license or even no license at all. Let's assume you want to make your contributions only available under the GPLv3. You would then include the terms of the GPL in a separate file like COPYING, and update the main LICENSE file to show both the new license and preserve the old license:
SoftwareName - this line briefly describes the software Copyright 2019 João Lucas This program is free software ... [GPL license dedication] -------------------------------------------------- This software is based on SoftwareName from <URL to original repository> under the terms of the MIT license: Copyright 2011-2018 Original Author Permission is hereby granted ... [MIT License]