"Adding flavor" suggestion
Byzantine army was one of the most diverse and “colorful” armies in 13th century.
They were using a huge of different other culture mercenaries nevertheless counted as the regulars (Varangian guards are a good example) – and supplied them with some Byzantine equipment. Lots of Slavs and Europeans also were enlisted in the army.
A suggestion is to give Byzantine lords a possibility of hiring the special “xenos” troops in conquered Slavic (Eastern European) and European settlements. Those mercs were a “cannon (or sword

) fodder” of the Empire so all settlements (even castles) should provide infantry only – the cavalry (elite) is left for the native Byzantines.
They could wear the initial equipment but with some “Byzantine flavor” – like the Eastern European spearman dressed in initial armor wearing a Byzantine helmet or European swordsman in Byzantine mail and kettle hat.
Some names for the troops:
Slavikí lonchofóros – Slavic spearman
Slavikí xifomáchos – Slavic swordsman
Slavikí kitharístas – Slavic axeman
Slavikí toxótis – Slavic bowman
Evropaïkó lonchofóros – European spearman
Evropaïkó xifomáchos – European swordsman
Evropaïkó kitharístas – European axeman
Evropaïkó toxótis – European bowman
Mesaionikó toxótis – Crossbowman (literally – “medieval bowman”)
Dóry me pelékis – Billman/guisarmer (literally – “spear-with-axe-man”)
Some Greek names\titles:
Politofylakís - militia
Taktikés – regular
Veterános – no translation needed

Afrókrema – elite
Archontas – lord (but better to use “strati̱gós”)
Aftokrátoras - Emperor (but mostly a ruler of Byzantium was called “Vasiliás” (king))