Adding a Cob or strawbale extension to an existing traditional home?

Hi everyone,

I've been reading on here for awhile but just now decided to seek some advice. My wife and I are considering buying a handy-man special in our area, and excited to give it new life. We have, for awhile, wanted to build with cob or strawbale. What I am wondering is this. If we buy the traditional home would it be possible to build an extension using either of these materials? To explain better this is what I have in mind. We would essentially add a shell to three of the outer walls, south facing, east facing, and west facing. The north facing wall would remain the current wall.

My thought, and I am very inexperienced and open to advice, would be to dig a second foundation outside of the current one and build a single story addition from cob or strawbale onto that foundation. My primary concern is can I connect the small back north facing portion to the existing wall. The house exterior is a wooden frame style and was built in 1920. The wall would only need to touch the existing house at the back. I am attaching a quick sketch of what I am trying to explain, in it the red lines represent the cob addition I am considering, the white space between the red lines and black lines represents future living spaces. Once again this would only be 1 story and would have a flat living roof and/or roof deck on top. The existing structure is two stories but this addition would remain one story. The basic question then is can I even do this? Can I attach the natural wall to the old wall somehow?

Thanks in advance for anyone that has any advice!

Best Wishes,
Shawn