Not sure why you want subdomains, but assuming you want to provide access to different companies under different subdomains (client1.domain.tld, client2.domain.tld etc.) I think it would be best to install separate FA instances, configuring each with a separate database.
If you'd rather use one database with multiple companies, you should be able to point all the subdomains to the same FA instance and edit the login page to select the company based on the URL of the request. That would probably expose the other companies through the backup script, though. Not to mention the mess that you would face if one client decided to restore the entire database, overwriting whatever had been entered by the other clients.
For a really complicated solution, you might be able to share the code through some file system trickery, while keeping separate configuration files. But that would most likely end up being more confusing than anything else.
Unless you had enough clients/companies to justify the effort, I would go with separate instances.