We found them to be coming from the same email address. Even when we removed the customer from our system, they'd create a new profile with the same email. To solve the problem in the short term, because they insisted on using the same email every time and were being absolutely relentless - whenever they logged in to a profile with that email, I redirected them to a dummy checkout page. That bought me enough time to write some rules that if someone makes more than X simultaneous connections, it blocks their IP and presents a "please call us" message.
They've tried about a dozen times in the last couple weeks, and they keep shutting themselves down by trying to scale up to a ridiculous number of connections.
The behavior seems strange. They insist on using the same email address and they do nothing to change their approach.