I tend to believe that Beckmann rearrangement for such compound will not take place because it is not energetically favorable. The rings of the reactant provide a very stable system because of the conjugation.
An example of how preserving aromaticity is favorable over Beckmann rearrangement is: the oxime of cyclohexenone with acid forms aniline in a dehydration – aromatization reaction (called the Semmler–Wolff reaction or Wolff aromatization); for details see:
Based on the following patent which does the Beckman rearrangement next to a substituted aromatic system I would say this is possible! http://www.google.com/patents/EP1229913A1?cl=en
You might have to carefully select the reaction conditions (and hydroxylamine derivative) to avoid cyclizing the oxime derivative of the 1,2 diketone into yet another ring system.
The problem is not to get the rearrangement next to an aromatic ring, and not from a 1,2-diketone - in both cases the Beckmann rearangement in well-known. But, aethiopinone is a 1,2-naphthochinone, i.e., an aromatic system. The Beckmann rearrangement in this case would mean the loss of the ring aromaticity, so, as Rafik has written, is hardly possible. In order to perform a chinone transformation in this case it would be easier to cleave the o-chinone system into 2 acids and functionalize them in the desired way.
Ammar, I tend to agree with Rafik and others in saying that such reaction is highly unfavorable and it is unlikely that this arrangement would take place for the reasons mentioned, unless very harsh conditions are employed.
When 1 , 2-diketones are subjected to Baeyer-Villiger reaction, anhydrides are ... of ketoximes to N- substituted amides is known as Beckmann rearrangement.
We have recently reported a similar reaction, the expansion of a porphyrin beta,beta-dione to an imide (Akhigbe, J.; Brückner, C. Expansion of a Pyrrole in meso-Tetraphenylporphyrin to a Pyrazine Imide Moiety Using a Beckmann Rearrangement. Eur. J. Org. Chem. 2013, 3876–3884. DOI: 10.1002/ejoc.201300274). So I would also guess your dione to ring-expand, but the regiochemistry of the reaction is not that easy to predict. Neither was the fact that the non-metallated porphyrins would undergo ring annulation reactions. Also depends on which oxide you form. We found 1,2-dioximes not to form readily. Good luck