O’Brien’s dog, n. — Green’s Dictionary of Slang

O’Brien’s dog n.

[he goes ‘a little way with everyone’; presumably a lost anecdote]

(Irish) one who is all things to all people.

1996

RTÉ TV Prime Time 23 Jan. [The Minister for Finance was] Trying to be like O’Brien’s dog, goes a bit of the way with everyone [BS].