Co-Branding

Hello! Not sure if this is possible BUT I have a site that I am shutting down because it is being ‘absorbed’ by the other. (basically it was a members site and now it’s becoming a product through the other one). I’d like my customers who go to the old site to see the second site but it’s branded as the first.

So – Site 1 will become Site 2 but still be branded as site 1. (basically I’d like a different header – maybe 1 different widget on the footer. The rest of the content will be exactly the same.

Is this possible?