It seems that here in the USA, most cob structures are kept on the small side. If you go to Eire, Scotland, or Wales you can find larger homes, several hundred years old that are built of cob.
I think the main problems with it here are;
1) the necessary
wood support structures
2) the thickness of the walls (needed to support the structure)
3) the obvious, time and manpower needed to complete such large structures
4) building code problems.
In Eire a two story cob house will have a lower wall thickness of at least 2 feet (62 cm) and slowly taper to a top of outer wall thickness of 1 foot (31 cm).
The corners, upper floor and roof would be supported by a Timber Frame, the doors and windows would also have wood frames with the cob used as fill in material much like the old Tudor wattle and daub style homes except that the structures would be completely covered with the cob.
Some of the houses in these countries that look like they are solid cob, actually have a core of stones, but the few I've seen that were cob, were indeed all cob over a wood frame setup. They also had Thatch roofs.
I've seen photos of one two story house in Australia that is around 200 years old and is 1200 sq. ft. plus or minus. It is cob over wood frame also but has been fitted with a modern metal roof now.
I think it is definitely a doable
project, given you have
enough manpower to complete it before the rainy season begins. or at least have it covered by the roof prior to the rains starting.