For an Ohmic conductor (not a semiconductor) the number of conduction electrons is constant. It is the drift velocity that increases as a larger potential difference means a larger acceleration between scattering events. You can change the resistivity by changing the temperature. This will change the scattering probability, hence the time interval of acceleration hence the drift velocity.
Of course you can also change to a different material, which will have a different resistivity for example because it has a different conduction electron density and mobility.