Generally, the PPC services do not provide for this. However, you can sign up as an affiliate for a site, and they will usually ask what site you are going to use for the affiliate links. Once you have that done, you can usually (but not always) forward traffic from a different domain directly to the affiliate site. Of course, relevance is the key.
I did this with a cosmetics site through Commission Junction. I found it was not worth the trouble, however, as I made just as much $ sending my cosmetics type-in traffic to Domain Sponsor. With a different affiliate and different domain names, you might have different results.