Well, you have at least for a time the continuation of Late Imperial "domesticity" thay you can find, in different shape and evolution, in contemporary Francia.
Of course the palatine dignity with ranks in court (axìa) changed a lot with time : quoting Louis Bréhier
Governemental management was attributed, depending on circumstances and sovereign's will either to private service agents (cubiculum) or financial public servants.
This lack of stability is actually one of the distinctive mark of byzantine administrative organisation. It happened that, with centuries, many fonctions were transformed in honorifying distinctions given as prizes. Offices of pure domesticity [koubouklion], as imperial changing room, became simple dignities attributed to civilian and military responsibles
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Roughly, you can distinguish several periods, for what I gathered, but the changing nature of the administration prevents, IMO, to really give a fixed hierarchy, and giving the spawn of the Byzantine Empire, chronologically...
Have you a particular period in mind? I'm more knowledgable about the first period, up to the VIIth, but I can try digging it out.
The
Magister Officorum, replace praetorian prefects by the IVth, managing both the imperial house strictly speaking (with
magistri scrinorium, originally modest managers of
scrinia, offices, gaining in importance) but often get the leadership of
scholae (palatine guard), public post (
cursus publicus),
agentes in rebus (sort of state police, roughly) and a lot of other political charges.
The
Questor Sacrii Palatii, originally managing the imperial chancery proper, became a huge part of imperial judicial and legal power, having reponsability of imperial ordinances and managing legal matters.
You didn't have one financial organisation at this point, but you have comes and procuratores charged with somptuary expenses that eventually included public and imperial works and financing.
Private domain of the emperors, to not be confused with fiscus, public land, were managed by public servents of
rei privatae (private matters), led by a comes with subservient magistrii.
The
praepositus sacri cubiculi or
parakimoenos, the ennuch charged with imperial domesticity became an important officer at this time (up to recieving public honors), as you can see with Eutropos, replacing matters so fat managed by
comes rei privatae.
Castrensis managed up to the VIth century the imperial household proper and who compoded it,
ministeriales that mixed both people as workers and
tabularii (accountants).
I'm sorry I can't take the length of covering every period, but it would be a bit messy. As you can see, you had an imperial domesticity/public office mix, that neither phagocyted each other, but were more complementary.