Upon studying Newton's second law, I noticed that it seems less of a physical law i.e. outcome of some experiment, than something we built upon how WE define mass and force.

The ratio of the masses $m_{1}/m_{2}$ of two bodies equals inverse of the ratio of their accelerations $a_{2}/a_{1}$ if the same force is acting on both.

A unit force is defined to be the one necessary to accelerate a body of unit mass by 1 ( m / s ) / s.

My question: Why can't we define the ratio of the masses as some function of the inverse of their accelerations, say ( the same ratio ) 2 . Or maybe we could have negative masses, if the ratio of masses equals negative of the inverse of their accelerations.

Is it just because when we have two bodies of the same mass, we want their total mass to be twice their individual masses? Is it just for having a simple expression for the law?