For a given metal, light below a certain frequency will not eject an electron. Once the threshold or minimum energy is met to eject an electron, what happens as light frequency increases past the photoelectric work function? Do more and more electrons eject from the metal and thus the metal becomes increasingly positively charged? Or is there little difference in the number of electrons ejected (and hence charge of the metal) after the threshold frequency is met?
Do more and more electrons eject from the metal and thus the metal becomes increasingly positively charged?
Yes , more and more electrons will get ejected when you increase the frequency of the light.However, the rate of emission is still the same. Moreover in the experiment the metal is earthed to maintain electrical neutrality so that minimum energy required to eject an electron remains same i.e $h \nu_0$ remains same.
The only difference you will observe by increasing $\nu$ that electrons that are ejected (photo electrons) are ejected with higher kinetic energy.Number of photo electrons ejected per second remain same as intensity of light remains same.
The reverse happens when you change the intensity of light but $\nu$ of light is unchanged.