# Change mesh density of Graphics3D object made of Triangles

I am new to mesh discretisation on Mathematica. I have a Graphics3D object made up of Triangles, that I would like to convert into a MeshRegion object using DiscretizeGraphics (see https://reference.wolfram.com/language/ref/DiscretizeGraphics.html).

In particular, I would like to control the mesh density. The above link tells me to use the MaxCellMeasure option, but it doesn't seem to make any difference to my graphics!

Thus,

Table[DiscretizeGraphics[g,
MaxCellMeasure -> {"Area" -> m}], {m, {0.3, 0.01, 0.001}}]


gives:

As you can see, the meshing is unchanged. It doesn't matter if I replace "Area" by "Volume" or "Length".

Can someone please tell me how to do this properly? Is this happening because my Graphics is already made up of triangles?

Using one of the solutions recommended here, I applied DiscretizeRegion with the MaxCellMeasure option to the meshed object produced by DiscretizeGraphics:
mr = DiscretizeGraphics[g];