Allowing the public to generate a CSR from your private key

As a hosting provider, I'd like to make the process of generating a certificate for a customer's domain as convenient as possible.

I was pondering creating a webpage where anyone could:

• generate a CSR for a given hostname from our private key


• take that CSR away and return to us with a certificate

Is there any danger in allowing anyone to generate potentially thousands of CSRs based off our private key?