It looks like there are 3 basic kinds of roman titles:

"Military" (generally requiring high command and/or some specific unit command traits):

Comes Domesticorum Equitum
Magister Equitum
Magister Peditum
Magister Militum

"Governnor" (generally won by having 5 or more loyalty plus some other positive mamangement trait):

Comes Dispositionum
Magister Memoriae
Magister Officiorum
Magister Scrinii

"Super loyalty" (won by having 7 loyalty):

Amicus Principis

It appears a single general can only have one title from each category, meaning they can get as many as 3 with Amicus Principis.