A-Albionic "conspiracy" theories claim basic conflicts amongst the factions of the ruling class instead of the more common "Master Conspiracy Theories" or "Unified Ruling Class" theories."
Excerpt from "Everything is Under Control" - by Robert Anton Wilson (Full book PDF)

The most plausible of the multiconspiracy theories--i.e., those scenarios that do not claim that one super secret criminal gang rules this planet, but rather that at least two such "gangs" exist, at war with each other--comes forth from an outfit styling itself A-Albionic Consulting and Research, in Ferndale, Michigan.
A-Albionic began in 1985 with a common or garden-variety uniconspiracy theory, blaming everything on the British royal family--rather like Lyndon LaRouche, who may have served as their original inspiration. In 1989, however, A-Albionic revised their model of the world (yes, they actually use the scientific word "model" and show other signs of some technical education). The post-1989 A-Albionic scenario holds that, in their own words (capitals included), "The Overt and Covert Organs of the Vatican and the British Empire are Locked in Mortal Combat for Control of the World."
A-Albionic traces this Mortal Combat back to the reign of the first Queen Elizabeth, when Protestant-Catholic warfare raged all over Europe--the time when the English, typically, made their pioneer scientific rationalist, Sir Francis Bacon, a high government official, while the Vatican took their pioneer scientific rationalist, Giordano Bruno, and burned him at the stake. The British Crown and the Throne of Peter have continued to make war on each other ever since, in this model, and every other "interest group," "trade union," "association of manufacturers," Mafia family, international bank or intelligence agency--everything that might qualify as a conspiracy in anybody's mind--have all become puppets, unknowingly, in this megastruggle. Thus, the Windsor Family Mega-Conspiracy manipulates a motley crew, which A-Albionic sums up as "Comsymp-International Banker-Judeo-Masonic-Labour Party-British Intelligence-SocialistInternational-Social Democrat-Fabian- AFL-CIO-UAW-KGB"--the same unlikely bedfellows that appear in many anti-Illuminati theories. The Vatican, on the opposite side of the world power struggle, controls an assembly of "CIA-Fascist International-Georgetown Jesuits-McCarthyite-Buckleyite-Knights of Malta." (See Knights of Malta and P2.)
Duo-conspiracy theories, like uniconspiracy theories, often lead to logical conclusions that seem bizarre to outsiders. Thus, the late Carroll Quigley, professor of history at Georgetown University, appears as a member of the Insiders in the John Birch Society theory, and these alleged Insiders, who sound a lot like the Illuminati, all belong to the British Royal Family Jumbo Conspiracy in A-Albionic's system. In fact, many right-wing theories become compatible if one identifies Insiders with Illuminati and both with international bankers (Jewish, Dutch, or whichever suspects you prefer). . . . Ergo, Quigley was an agent of the Windsor Gang.
But Prof. Quiqley taught at Georgetown, which the Jesuits own, so this makes him actually a tool of the Vatican conspiracy according to A-Albionic. He had entered the Windsor-Insider-International Banker-Illuminati conspiracy, A-Albionic says, but only to expose it. Quigley's book, _Tragedy and Hope_, usually cited by right-wingers as "inadvertently" revealing the Insider's plot for world government, had nothing inadvertent about it at all. The Jesuits sent Quigley to spy out the enemy and publish their secrets, according to A-Albionic.
This minor detail in the conspiratorial mosaic became a matter of passionate debate among conspiriologists during the 1992 presidential race, because Bill Clinton, in one speech, mentioned Prof. Quigley as a teacher who had vastly inspired him in his youth. To the majority of right-wing conspiracy buffs, this "proved" that Clinton worked for the Insiders, or the Illuminati or at least the international bankers. But A-Albionic insisted on their own analysis. If President Clinton really received inspiration from a Jesuit school, they claim, then he has become a tool of the Vatican/CIA, or anti-Illuminati, conspiracy.