[tkamiya]

Here are my suggestions and reasoning behind each. This is what I would do in my own darkroom. Because of the way it was worded, I'm assuming OP's prints are reasonably close, not way off, from being good. Once I get my prints reasonably close to right and start perfecting it, more formalized process doesn't work for me.

If my blacks are both too grey, and my whites are too grey, I suppose you can switch to the next-highest contrast grade and use the same exposure.

I'd use the next higher contrast grade and the same exposure timing to start. Tones below mid gray will move lighter and tones above mid gray will move darker - increasing contrast. Once I have the right contrast, then I'd re-evaluate the exposure timing.

I make a print that needs more contrast. I find that the blacks are black enough, but the whites are grey. I switch to the next higher contrast grade. Should I change my exposure?

I'd use the higher contrast grade filter. Then reduce the exposure a bit. Otherwise, you'd start losing shadow details due to darker grays moving towards black.

My current print has fine whites, but the blacks are too grey. I could increase my exposure to make the blacks blacker, but suppose I judge that that would wash out my highlights. I changed to the next highest contrast grade. Should I change my exposure in this case?

I'd use higher contrast grade, then increase the exposure timing. Otherwise, highlight detail will be lost.