Is it possible to convert an octagonal electrical box so that it can house 2 Duplex outlets without changing the shape of the box?
This product by Hubbell is about the only thing I can think of that will provide the equivalent of a two-gang duplex (quad) receptacle on an octagon box. 

http://ecatalog.hubbell-wiring.com/press/pdfs/H4416R.pdf



Amazon.com even has them: http://www.amazon.com/Hubbell-HBL415BK-4-Plex-Receptacle-5-15R/dp/B00NGPR9MI/ref=sr_1_15?ie=UTF8&amp;qid=1440803585&amp;sr=8-15&amp;keywords=hubbell+4-plex