Jick Duck, I guess almost anything is doable if you are sufficiently motivated and take the time and money to make it happen.
To get everything in one box you could go the very expensive route as follows:
Eko Systems http://www.openlabs.com/
Wersi & others
These approaches my satisfy your objects but it will come at a high cost.
Another approach is go about it with separate modules:
Roland A37 midi controller or other
Shuttle computer with an excellent soundcard http://www.shuttle.com/
After all this you would need to get your choice of software some of which has been discussed in this thread.
I hope this helps.