You can over-dye the wool pretty easily. I've had no problem over-dyeing colors, just take into account that the new color will shift, so if the original is a light grey, the new color will have a greyish tint, but if the original were say a yellow, and you tried to overdye it blue, you'd get green. So the principles of color-blending still apply.
I only dye with food-safe colors, food coloring, Kool Aid, that kind of thing, and you can get lots of beautiful colors that way. You can take a look at my blog or etsy stores to see some examples. I'm not willing to use chemical dyes at this point, since they can be dangerous.
As for whether to dye then frog or frog then dye, it's just a matter of preference. It would probably be easier to frog it first though, because if it felts just a bit as a yarn it's not a big deal, but as a sweater, it makes it more difficult to later frog.
Honestly though it's nearly impossible to get a solid color dyeing by hand. There will always be variations in color, whether from different areas of the yarn having different exposures, or even the slightest bit of dirt impeding dye uptake. What I do is make it look intentional rather than accidental, by dipping it unevenly, leaving some areas lighter than others.