Electronegativity, more than two bonded atoms

[Ordinis]

If we have a molecule where an atom has one bond with another atom, does the electronegativity change for those atoms then? If we were to bond one of the atoms once more with another atom, (if we presume it's possible) would the electronegativity then be changed for that atom since it's bonded with another atom already? Or is the electronegativity constant?

[mdv]

Electronegativity is a constant. What changes when a second, third, ... bond is formed is the relative dipole orientations between the bonds due to changes in geometry and the net dipole moment of the molecule.