Hello,
Do you want to copy that company's existing Magento store to another server under another domain? I do not see any problems with that. You just copy files and database and update configuration to a different domain.
It's possible to run multi-domain setup from the same Magento instance but this is a bit more complex and they will have to allow remote access to store's database which can present security problems if not done properly. Also, in this case, if both stores are not in the same data center, your store will be slow because database connection can not be done via local network.
If you want to run multi-domain setup, it should be done in the same datacenter which allows local connection from one server to another. If this is not possible, the only option I see is to copy the store to another server and change its configuration to run from a different domain.
hope this helps.