Hey there, its not hard to find foreign mercenaries that fought for the Byzantines but do you know of any instances of Byzantine forces acting as mercenaries? Just thinking that with the skills of their cavalry/archers/navy, and all the civil wars they had, there had to be atleast a few units that struck out on their own.
The thing about the Byzantines is that there’s a succession crisis every Tuesday. It’s really a miracle that they outlived their nemesis, the Caliphates. So the answer to this is sadly no, not any we know of.
This is the same case with the Romans. Sure they could hire themselves out but because the Roman/Byzantine identity is so strong, why hire themselves out to some foreign power when they can become the power themselves? They speak the language (Latin/Greek), they likely are from there themselves, and they already have a strong military tradition they could use to train themselves.
The whole concept of “striking out on their own” likely isn’t a very alluring prospect either. Today any bloke can go to the local French Foreign Legion or join Blackwater/Xe Services, and still keep in touch with their loved ones over the Internet assuming the contract says it’s a-okay. Sure a Cretan archer can go serve the Legions in Gaul but chances are they’ll still return to their homeland which usually isn’t embroiled in imperial struggles.
You may however may be interested in the story of the Catalan Company, an actual Spanish mercenary company that got betrayed by the Byzantines and ruled over Athens for a short while as their own dynasty. Just like the ancient Barcas who ruled over Spain and whose most infamous general, one Hannibal Barca, brought his elephants to the Swiss Alps for a vacation that one time.
Thanks for the question, anon.