If there are many objects moving in many directions, you won't be able to find a reference frame in which the mass of the system is equal to the sum of the rest masses of the objects.
A reference frame is definitionally a point from which you would measure an "apartment mass". The rest mass isn't relevant to a reference frame where that mass isn't at rest. This is true at all scales.
A reference frame is definitionally a point from which you would measure an "apartment mass". The rest mass isn't relevant to a reference frame where that mass isn't at rest. This is true at all scales.