
Unless there are obvious fights between two dogs - usually in same sex situations and more often than not two bitches, 'rank' has IME little or no place in a domestic situation, i.e. house dogs which are equal family pets :) Yes, you may find one is more pushy for attention than another and if you choose to fuss that one first that's your option however, all of mine bounce off one another in a scramble to be '1st' - there's no clear leader LOL.
A very good friend of mine only kept males, between 5-7 and all used at stud. There was an 'alpha' male among them, the quietest and calmest of the boys and he took on this mantle at around 2 years and retained it into his teens :) Never saw him fight or scuffle - he just appeared to 'give a look'.
Now when this lady got dogs back for rehoming (she helped with a couple of breeds rescue) the new arrival always got fed FIRST - flying in the face of alpha, then beta etc as the text books would have us believe. Her reasoning was that a newcomer didn't have a status and she didn't believe in creating the potential for issues by allowing any jostling for position among the residents - the other dogs of her own were fed in no particular order at any other time.
I think there's a lot to be learned from not making the assumption that dogs
need a hierarchy - IME with my own and friends' dogs it leans me to believe that in most instances they don't :)