On a DNS level it is possible.
Right now we have a wildcard DNS
*.quickfile.co.uk
Let’s say you wanted to handle www.example.quickfile.co.uk, you’d need either one of the following A records on your DNS:
*.example.quickfile.co.uk
www.example.quickfile.co.uk
In each case you have the first sub-domain hard coded (.example), so you’d need a record like this for every account on QuickFile. this is impractical as it means we need to apply DNS changes for every new QF account, resulting in 10s of thousands of A records.
Even if we handled the provision of A records I couldn’t say for certain of our SSL certificate would resolve.