Well, it looks like going to every one against every other scenario 
Maybe.
That Caldari/Minmatar alliance is looking better and better. Jovian favorites, UNITE!
(Though it's going to take some creative writing to get the Amarr and Gallente into bed.)
Thought #1: CONCORD, never wholly recovered from the Elder attack (and the Sleepers, et cetera), realizes that it can't continue to limp along as it has been doing. Perhaps this realization is driven home by the Republic's forging a formal alliance with the State, and the two of them deciding that they will no longer be bound by CONCORD authority. (And perhaps the State also decides in whole or in part to forget about all the financial support the Empire poured into it.)
Thought #2: As a side effect of its conflict with the Republic/severing of diplomatic relations, the infrastructure of the Federation deteriorates. As a whole, it'd grown heavily dependent on automation and immigrant labor (and immigrants to maintain that automated machinery), and many of those immigrants are fleeing the Federation. Food supplies begin to be disrupted even on self-sustaining worlds, causing outbreaks of famine in some areas while in others crops rot in the fields or hydroponic installations. While appeals to patriotic sentiment do get some Federation natives to take on this work, it's not enough. Government attempts to conscript labor go poorly. Riots happen.
Thought #3: The Empire, who has long been a trading partner with the Federation despite their core ideological differences (
http://wiki.eveonline.com/en/wiki/Gallente-Amarr_Free_Trade_Agreement), quietly steps in to provide assistance. This may not be done at the Emperor-President level, but negotiated between corporations. For example, the food situation may be dire enough that Combined Harvest (despite their being paranoid bastards) negotiates with Nutura for the use of transport ships and labor gone idle from Nutura's State and Republic operations.
Thought #4: The negotiations between Federation and Amarr corporations are often initiated with the assistance of Quafe representatives (
http://wiki.eveonline.com/en/wiki/Girani-Fa_incident), because Quafe, despite occasional sordid commercials and pesky rumors of ingredients sourced from biomass, is still held in good regard by both Federation and Empire. As Quafe's role of emissary grows, it finds itself increasingly divided between diplomatic and profit functions.
Thought #5: Yielding to shareholder pressure, Quafe transfers its diplomatic function (and a chunk of sponsorship money) to the remnants of CONCORD, who then takes on the role of negotiating and preserving the economic alliance between Federation and Empire. Only then does the alliance become acknowledged at the highest levels.
