It is quite common to be descended from multiple Mayflower passengers. The "dating pool" wasn't very big in those early years, so there was a lot of intermarriage between the families. I have eight myself.
As far as the "degrees," if you are looking at relationships through siblings and marriage, that opens things up even further. For example, George Washington did not have any biological children, so to have any connection with him it would have to be something other than a direct relationship.