That is an interesting question. I will do some research. My initial thought: for big game such as deer there is no "possession limit": if you can legally kill a deer in 10 states, you could legally possess 10 deer. For waterfowl which is federally managed, most interpretations would conclude that one "aggregate possession limit" does indeed add all U.S. kills together. See page 6:
http://www.fws.gov/le/pdffiles/50_CFR_20.pdfUpland birds are probably more like big game, in that each state's limit would not be counted toward another state's possession limit. This assumes, of course, that it could be clearly demonstated from which state the species in one's possession were legally killed.