Can I fit normal kenwood bowls in the major series
I've put regular ceramic bowls under my mixer before (also a Kenwood, but that doesn't really matter.)

The only things you have to look out for are:


Does the paddle scrape the bottom? If so, raise it up until it doesn't (paddle height is adjustable.) 
Does the paddle hit the sides as it rotates? If so, your bowl is not wide enough. Get a wider bowl.


If you were mixing a very small amount, you might find that, due to the angle of the curve of the bowl, it is not optimum in getting everything amalgamated, but for the most part, a bowl is a bowl. Just like with the supplied bowl, you probably have to scrape sides every now and again to make sure everything's mixing together anyway.

TL;DR: a bowl is a bowl, just don't let the paddle hit it, because, well, the paddle is hitting it (if you needed a reason.)