Plesk Onyx (Latest versions) have composer integrated. You can access it in two different ways.
First
Trough the panel itself. It allows you to install dependencies from a composer.json file. This means that in Flarums case, all you need to do is upload the Flarum/flarum Git repository, scan for applications, and install dependencies. = working flarum.
Second
Trough a shell user which is NOT chrooted. (Allows all composer commands)
I currently utilize plesk for all my clients websites, and composer works well both ways. Although updates and installing extensions are much easier with the second method... The first method is possible, but you have to manually edit the composer.json and add them to required dependencies.
Plesk Composer Documentation
What license do you have? Is it a self-managed VPS (Do you have access to root)?
