What happens to the acceleration of a system when the mass of the system increases but the net force stays constant?

What happens to the acceleration of a system when the net applied force increases but the mass of the system does not change?

Use F = ma

As a constant force F is applied, ma must remain constant.

However, since m increases, a should decrease to maintain ma constant.

Use F = ma again.

Mass is constant, so, F/a must be constant.

As F increases, a should increase as well to keep F/a constant.