I want to know about the equations of a motion that has a specific acceleration in all three dimensions simultaneously. which requires vectors that simultaneously are accelerating in all directions.

Vector sum gives magnitude and direction for acceleration.

let me put it this way. can there be such motion? i understand that currently there's no theoretical basis for this. so i just want to know is it possible to have an acceleration of A designated to all directions simultaneously? and not for the metric itself. for moving body!

An expanding object such as a balloon the surface of the balloon certainly counts as an object and once you blow air into it. It accelerates outward from rest in all directions simultaneously.