I recently looked through SO to find the answer to the same question here, but there was not an answer directed at the question in regards to the risk of doing so. But basi
AsyncTask(), with the exception of the Honeycomb releases, execute serially. So, no, you cannot execute another AsyncTask() from within doInBackground() -- I guess I should say that I've never tried it, but it's highly unlikely you're going to achieve the desired affect.
I asked about AsyncTask() execution during one of the Google Office Hours. Straight from their mouths when asked, "Why did it change from serial to parallel and back to serial execution?"; "Because it broke a lot of stuff."