Blimey Steve, I didn't know anything about these locos.
Is this what you're talking about? ...
youtube link
I guess that shunting is the most likely reason for having a set of controls " at each corner".
A bit like our class 20 where you can turn round in the cab to go the opposite way.
I suppose the CIE A was designed as what the Americans call a 'road switcher', ie a loco that both shunts and hauls loads on the main line.
Hmm. BW