Leni — yes, you surmised correctly. I had missed the supporting arm in the first photograph.
Yes it is still absolutely 100% Walsh Primrose W9691. The added bits don't change that. Please ignore all my previous waffle about it possibly being a single — this has to be from a four flute epergne minimum, with a central metal or glass connector.
First time I have seen evidence that Walsh made this type of epergne ornament, although I am not at all surprised.
Nice one, Leni. Apols for leading you slightly astray.
Bernard C.