You have a master source file that you want to translate into multiple languages. However, you also want to create a new form of English (based on the tone or the different levels of formality) that is not currently available. So, you want to create a new source file based on the master one, using just Transifex.
All you need to do is to follow the steps below:
Upload your master source file on Transifex.
Add all the desired translation languages to your project to translate your content.
Use one of the supported English language codes (en_US or en_GB or en_GR etc..) as a target language by simply adding this to your project as well. Note that this language code will be related to the new form of English regardless of geographical, political, or cultural criteria.
Use Transifex to "translate" the master source file to your new version of English.
When the above "translations" are completed, download the "translation" file from Transifex.
Create a new project, and under this, upload the new English file as a source file.