is there a link to the supplemental register?

No, there is no link to just the "Supplemental Register." The Supplemental and Principal Registers are not two physical "registers" and now would only really be accessed online. The following link is to a basic search engine on the USPTO website for searching all 4 million-plus marks minus registered or applied-for marks that have been dead for decades. You might be able to conduct a search for registrations specifically on the Supplemental Register and I and probably many other trademark attorneys on this site or elsewhere can construct a search like that in the freestyle USPTO search engine. But I would expect to retrieve hundreds of thousands of marks which obviously could not be reviewed. Basically, any knowledgeable trademark attorney could conduct a search of the USPTO register and possibly other databases to give you their best assessment of the distinctiveness and potential rights you or another party could have in a particular mark. But you need to retain that attorney to do that.

i'm confused. you referred to a link and there is none. are you saying the principal and supplemental registers are combined?

The link disappeared upon submission for some reason. Perhaps this web page won't accept a link in the comments so I'll try to put it in the Answer section. Yes, for all practical purposes in terms of looking up registered marks, the Principal and Supplemental Registers are combined into one "Register" which is actually the USPTO database of applications and registrations accessible to the public on its website.

It looks like this question can't be answered anymore. You can send me an e-mail at abutterman@s-n-h.com and I'll e-mail them to you. Or just go browse the www.USPTO.gov website.