Can the effects of the higgs field be saturated?

jerich1000

Velocity through an orifice follows a certain equation until the fluid approaches the speed of sound; magnetic fields obey certain equations until the magnetic material becomes 'saturated'; gasses obey the ideal gas law until the gasses atoms become too close to each other.

There are many examples in science where behavior within a field changes after a 'certain point'.

Is it possible for sufficient mass, such as mass of degenerate matter, to overwhelm the higgs field locally such that surrounding matter is slightly less massive? Or could the interior of a volume of degenerate matter be lighter than expected based on the higgs field being partially soaked up by the outer layers of such matter?

Thanks