And to follow this up just a bit...
To maybe just clarify the switching/saturation concept a bit. When you reach this point in transistor operation... there would no longer be a relationship between base current and and collector current. Once a transistor is fully conducting, adding MORE base current has no resulting effect on the output. You have left the operating region where an analog (or proportional) relationship exists between the base pin and the other pins. While you can overdrive this state to gain some wiggle room to "stay" in saturation state... adding a much larger than necessary base current can also have the effect of harming the transistor.
This is why many of us cringe when we see a diagram containing BJT that neglects to use base resistor to limit current to a safe value.