Multiple domains on the same website

[jimhoyt]

I have multiple domains that all point to the same website; these aren't redirected but remain the domain in use.

I installed SS on one of the domains, and it worked fine there. 
But if you use a different domain and go to the same directory I get the SS Installation screen asking for my License code.

After I do the set-up under the new domain, then I get the SS Installation screen on the one that was previously working.

How can I set this up so it works on all the domains that point to this website ?