In general usage, a consortium is a group of business or government entities allied for promoting some specific agenda. For example, "the standard is backed by a consortium of major industry players."
In the context of the Cassiopaean material, this refers to fourth density service to self parties and their human representatives. This is a shady agglomeration of big finance, the military-industrial complex, intelligence agencies and other players, where key figures are not known to the public or most governments even by name.
The below quote from Woodrow Wilson from 1912 probably speaks of something of the sort:
Since I entered politics, I have chiefly had men's views confided to me privately. Some of the biggest men in the U. S., in the field of commerce and manufacturing, are afraid of somebody, are afraid of something. They know that there is a power somewhere so organized, so subtle, so watchful, so interlocked, so complete, so pervasive, that they had better not speak above their breath when they speak in condemnation of it.
The various actual or hypothetic agencies whose names are often mentioned in discussions of secret government and conspiracies are most likely not direct members of such a consortium and may well be red herrings.