The Buddha taught that there is no such thing as a unitary self. Instead, what we think of as "self" is actually comprised of five elements, referred to as the Five Skandas: form (or body), perception, sensation (or feeling), habit (also called predisposition or karmic conditioning) and consciousness.
We perceive these five elements as an aggregate and assume they are unitary, but in fact they are like strands in a cable, each one separate and dynamic. One's body, feelings, perceptions, habits and consciousness are constantly changing and evolving. So there is no stable, unitary self, just individual threads that change color, shape and texture endlessly.
These separate threads of "selfness" are wound together in a way that we think they are one strand, but in fact they are distinct. Each of these "strands" is part of an infinitely larger tapestry woven together by causation.
As much as we like to think of our "selves" as separate, we are part of the tapestry, and we are as capable of separating our "selves" from "others" as a thread is able to unravel itself from the cloth of which it is a part.
Peace to all beings.