This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
I would say that regardless of whether it is possible or not, which I truly don't know the answer to, you should never need to. The point of an non-static inner class is that it belogs within the outer class. Period. If you want to make an extension of the outer class that has an inner class that extends the inner class of the super class, this is perfectly doable, however convoluted.
I've heard it takes forever to grow a woman from the ground