I don't really mind the Quaesitor sideline as it's interesting in itself, but...
Reading through HoH: Societas it seems that one reason there may have been single-house covenants for some Houses early on is that oddly they are loosely affiliated groups of disparate lineages in the 9th century.
Although Flambeau is commonly depicted as a somewhat monomorphic house, under Apromor there was a drive to recruit non-Christian magi, particularly Pagan Mercurians but this could also imply Basque sorginak (cultists of the goddess Mari) and other native French and Italian hedge traditions that would seem out of keeping with the structure of the House in 1220. A "Flambeau" House covenant (in the sense of a covenant dedicated to the ideology of one House but perhaps containing a few members of other Houses eg Verditius, Mercere, Guernicus etc) would potentially have a great deal of diversity, as even though it would not be "multi-House" it would be "multi-tradition".
A similar argument could apply for Tytalus, Jerbiton (perhaps more homogenous than the others) and of course Ex Misc when it forms.
The argument that multi-House covenants would be needed for stability and growth breaks down under this, as the different lineages within the nascent Societas would provide any needed flexibility, although discord may be a counterbalancing issue.
For instance, I see merit in Timothy's suggestion that a group of like minded magi of the early Order in a particular region that had strong links with Hellenic culture might band together and join Jerbiton, not because of any strong similarity in philosophy to the Iconophiles, but because of shared culture.
Similarly, many of the early French and Spanish magi might join Tytalus and Flambeau respectively because that's who they were coerced/recruited by in their native area - any differences between the various lineages becoming blurred over the intervening centuries as say Flambeau lineages with particular aptitude for smithing discover House Verditius and shift to becoming members of that Mystery House, Tytalus magi with a mystical bent switch to becoming Criamon of the Path of Strife or Jerbiton magi with strong political bent have their apprentices accepted by magi Trianomae and thus move their original lineage into House Bonisagus.
Diffusion between the Societas seems even easier - some magi would naturally fall between the cracks between Flambeau and Jerbiton and Tytalus easily enough into another House even before the spread of Ex-Miscellanea beyond the Brittanian Tribunal and likewise, magi leaving the Mystery Cult Houses would seem more likely to fall into one of the Societas or Ex-Miscellanea as needed.
In some ways though, these Societas "House" covenants would be the ones most likely to attract Bonisagus, Verditius, Merinitia, Criamon and Bjornaer with particular interests and thus have the potential to evolve into the first multi-house covenants, unless the apprentices of these guests shifted due to the reasons above.
Cheers,
Lachie