Hi
I do not profess to be an expert on the Spanish Civil War but I think the CTV units should only have Italian leadership and the Italian leaders should only lead Italian units.
Part of the problem with the CTV was its low quality leadership (particularly at a senior level) - I think that the current "mix and match" arrangement allows you to avoid/minimise this issue by using Italian units with Spanish leaders or by using Spanish leaders when there are insufficient Italian leaders.
From my reading it appears that the CTV operated under Italian leadership - sometimes in co-ordination with the Spanish forces, and sometimes seemingly acting independently.
Given Mussolini and the seniority and personalities of senior leaders involved I doubt that the CTV CIC (Roatta / Bastico / Berti) would have taken command and then handed over leadership of most or all of their troops to Spanish officers. After the Guadaljara debacle in 1937 Franco blamed the Italians and insisted that they operate in the future under Spanish direction and I understand that later Franco wanted mixed formations of Spanish and Italian troops led by Spanish officers - but I have not found any detail of this actually happening.
I would appreciate comments regarding this
regards
Mark