Question : Increasing mass and the gravitational field

Imagine this simpple case :

A spherical mass with rather low density under a gravitational condition,

resulting in a certain g factor at the surface and a dropping g-factor away from the sphere

according to Newton's inverse square law.

A gravitational field is formed of a certain strenght.

Now imagine that i could gradually insert into the sphere an amount of extra mass,

maintaining the radius and volume,

increasing thus gradually the density and the mass of the objekt, and the strenght of the gravitational field.

For instance mass x2 in the same volume > g at the surface x2, dropping in value further away.

> What is fysically happening then during this event, to cause the gravitational field to get stronger ?

We know the formulas for what is happening, we observe the resulting behaviour of the objekts,

but how could we explain this transition as a process ?