Everybody has 2 parents, 4 grandparents etc. Genealogists soon stop talking about "German ancestry" etc. You only need one marriage to branch off in a whole different direction.
JFK's mother was a Fitzgerald. The line doesn't seem to have been traced, but of course it'll go back to the Anglo-Irish pool which included the Burkes, Butlers etc. You'll find English wives in there.
And there are two sorts of Kennedys in Ireland - the native Irish Kennedys and the descendants of immigrant Scottish Kennedys. Apparently JFK's lot are the Scottish sort, and the Scottish nobility was also well supplied with English blue blood.
What's strange is how people talk as if their ancestry is defined by male lines.