Yes, you can now do this with the Beta Editor!
You can set up a deployment environment for each customer, each with a separate domain. Each environment can point to a different database, but they can all point to the same branch so you can upgrade them all at the same time. (Or, of course, you can serve different versions of your code in different environments. But the merge-fest @stefano.menci suggests isn’t a requirement!)
I know you’re big on the Uplink, so you might be interested to know that you can connect Uplink separately to each particular environment (each env has its own uplink keys). Or, you can create uplink keys for one environment, then check Share Uplink with other environments and call those server functions from any environment!
Your code can use the environments APIs to work out which environment it is currently executing in, and show appropriate branding and behaviour.
(Please do give us feedback on how this system is to use! “Multi-tenant with a domain for each tenant” apps is a pattern we want to make easier with Anvil.)