Don't think this is necessary for the following 2 reasons:
First, it may seem inconsistent, if the Satipatthana talks first in each chapter only about observation of objects which are subjective: my body, feelings, mental states and qualities - but then concludes that this observation may not only concern my own, but those of others too and on par.
But on a closer look this is only too natural and not really a contradiction, due to perceiving everything from our own perspective: Once an opinion is made, that my thoughts, feelings, fabrications and body are solid - from which a solid me can be construed - the same is also construed to be solid with others too.
But if through ceaseless introspection these are seen as ephemeral processes recreating them self, it would be very difficult to construe that it would be completely different with any other.
Therefore, the objects for observation outlined in the Sutta are only internal, and once this understanding has been developed internally - since nobody can avoid encountering others - this understanding can only comprehend the same externally, spontaneously.
Secondly, it has been my experience by only learning to observe internally at retreats, that the understanding developed therein couldn't be refrained from understanding the same with others externally too.
But I don't believe this would work the other way around. And it doesn't make sense to systematically include others in ones observation, as long as ones thougths appear solid, pleasurable and having anything to do with a self.
This is where advaita and buddhism have a huge difference...
In buddhism there's not me to make responsible for the appearance of thoughts, feelings, etc...
In Advaita it is said that behing all these, there is an everlasting, never-changing me.
I think the distinction is only that the advaida approach aims at ultimate existence - while Buddhist thought considers every existence ending with old age, sickness and death, and not really worthy to persue.
Beside this implications only showing up in possible after lifes, in everyday encounters the 'I' thought of advaita adherents also seems to transcents the common dichotomy between you and me.
However, though I mainly know about advaita only through encounters (and I can't be sure how pure advaita those encountered have been) if it comes to responsibility, I think in buddhist life it is imperative how ones relationship to thoughts, feelings, constructs are responsible for those reacreated after.
While in advaita, what for would a never-changing me could take responsibility for?
kind regards..