Ability to Automatically Move Customers to New Customer Groups

It would be helpful to be able to automatically move customers to a new group after they place their first order.

For example, we require larger order minimums for our new customers, but after they place their first order they are no longer required to adhere to these minimums. We have separate customer groups set up, but we'll have to manually remember to move customers from one group to another after they place their first order. It would be a huge time saver if customers were automatically moved. Our old website platform was able to do this.