The Modern English possessive suffix -'s is not a case any longer. Cases inflect nouns, but the -'s attaches to the end of noun phrases, rather than to their head nouns.
Technically, an affix that attaches to a syntactic construction instead of to a word of a particular type is called a clitic (a clitic can be either an enclitic or a postclitic, just like an affix can be a prefix or a suffix; respectively).
So, as an NP postclitic, -'s attaches to the end of the last word of the noun phrase whose head noun is the possessor. Thus, the Queen of England’s first great-grandson or the guy at the door’s keys, as tchrist points out -- it's not England's g'grandson, it's the Queen's; and they're not the door's keys, they're the guy's keys.
Thus, also, Somebody Else's Problem.
Indeed, as HHGttG makes clear, the SEP field is very advanced technology.