Like all the best questions,
the answer to this one is of
course... it depends!
If your cob is structural(holds the roof up all by itself) you certainly can't just knock down a wall without serious work to stop the whole dang thing coming down on you.
OTOH, if you have a timber frame(or whatever, something aside from just cob) supporting your roof, you probably can knock out just about any walls you want. Sure, it's solid and monolithic, but it's earth, not stone. You can take it apart with hand tools. And after you tear a wall apart with a mattock, the debris can go right into the mix for the new cob you need, instead of into a fire or dump like a stick-frame wall!
Easier yet, what about adding without knocking down any walls at all? Adding complete rooms would seem pretty efficient; a good sized eat-in kitchen with sleeping loft could be the entire house, to start with; rather than expanding by knocking down a wall, you could add additional rooms next to it, either by attaching to a secondary door, or by building in front of the main entrance and moving the entrance into the new room. Extra thick interior walls aren't really a problem unless you're dealing with fairly severe lot-size issues...
The main potential complications, as far as I can see, would be the roof and the foundation/drainage.
As far as the roof goes, in my area I see a lot of shitty add-ons to stick-built houses with terrible roof-lines. The original house is usually gable-roofed and single story, oriented with the roof sloping towards the street and back
yard. To add space as cheaply as possible a shed-roofed expansion is stuck to the back... but to have
enough headroom, the pitch must be unreasonably shallow, and the connection point is often very awkward looking as well as a potential leak spot. I've also seen the same thing with other types of roof; a pyramid hip roof added onto like this is dreadful.
Simply building a gable roof with the slopes facing the side yards would allow easy expansion to the front or rear. For a small structure I'm a big fan of a simple shed style roof, which is easy to expand in 3 directions.
Of course you could also build your initial room with some sort of roof that is not well suited to expansion as built, like a pyramid hip roof, and deal with expansion by lifting the initial roof to a height that allows proper slope of additional roof space. You could also build more roof than you need from the beginning, and enclose the covered space gradually...