MapPoint doesn't have true layers.
As you've found there's only one type of shading, so you can't (say) put
transparent hatching over pastel shades.
However, it is possible to plot more than one dataset on a map.
I have some samples here:
The most useful for you are probably the Airport Delays and possibly
2000 Florida Election.
What you need to do is to choose a different map type for the county (or
state, but I suspect the shading will look better on the State).
If you have a single value, you could use a shaded circle or a sized
circle. (I've used sized circles to show earthquake energy over a shaded
area map of hazard probability before).
In the Airport Delays map, I wanted to show two values per airport: the
number of flights, and the percentage delayed. So I used Sized Pie
Charts. Climate data was for the shaded areas. (does snowfall affect the
The Florida example plots lots of values on bar graphs for each county,
and it is probably a bit busy. I had to remove the Gore & Bush votes
just to get reasonably usable plots :-)
The shade gives an estimate of left-right leaning based on the ratio of
Gore:Bush votes. Yes, a year before "Red-Blue" States became popular
in the media, I had some maps of Red-Blue Counties :-)