I certainly wouldn't mix road tyres and semi's on a car at the same time. The grip difference is so great that it will cause a huge handling imbalance. If you're at a point where you need semi's on the back, then you'll need them on the front as well, else you're gonna see your ass.
I've had and used the Toyo R888's on my Focus for trackdays, autocrosses, A1 Supercar Parade, and a fair bit of road driving. Their cost was about the same as a good road tyre.
The semi's actually grip pretty well in the wet due to the soft compound, the R888's are actually listed as a wet weather race tyre, however they don't have much of a tread pattern and so are more likely to aquaplane than a normal road tyre if you encounter heavy rain or standing water.
The other trade offs are that the semi's are a lot noisier than normal road tyres due to the open tread pattern and that they wear out a lot faster than normal tyres. They also pick up a lot of stones and crap off the road, and the soft rubber is more susceptible to cuts and damage by glass and sharp stones and such.