Assuming that the Earth's atmosphere is a perfect sphere, then the atmosphere's center of mass will be at the point equidistant between Earth's poles (i.e. the center of the Earth!).

The center of mass of a sphere is its geometric center.

The center of mass of a soccer ball is its geometric center.

Mass is uniformly distributed about its center of mass.

The simplest answer is to add the mass at the center of mass. In that case, the total mass will increase, but not the center of mass. If the additional mass is not added at the center of mass, then it must be balanced with more mass at a location on the object that depends upon the object's shape. That's where things get complicated.