Generally you will only want to utilize one token at each step. So if you need to merge up claims, you will want to do that at the claims transformation step of the second STS.
So the flow would be authenticate with STS1, then authenticate with STS2 with the token from STS1. At that point you would pass through the claims and transform to add additional claims as needed. Then the resulting Token would be ready to consume from the RP application.
I have actually started a blog series about a really similar scenario that we recently architected. Not to be overly self promoting, but it doesn’t make me any money, so I’ll post it in case it is helpful.
http://www.livingthearchitecture.com/mixing-sso-with-existing-technologies/
I would be glad to go more in depth, but depending on the specifics of your scenario, the specifics of the solution will change greatly. I think the above expresses the general approach you will want. Let me know if I can help any more.