Here is a list of shared LA chief Execs. It is over a year old but might still be of interest, I assume some are out of date and there are probably more... but it is a start!
Charlie Adan is Chief Executive at both Babergh DC and Mid Suffolk DC.
David Buckle is Chief Executive at South Oxfordshire DC and Vale of White Horse DC.
David McIntosh is Chief Executive at Christchurch DC and East Dorset DC.
David Neudegg is Chief Executive at Cotswold DC and West Oxfordshire DC.
Joanna Killian is Chief Executive at Brentwood BC and Essex CC.
Kevin Dicks is Chief Executive at Bromsgrove DC and Acting Chief Executive at Redditch BC. I can't say if this arrangement is to be made permanent.
Mark Williams is Chief Executive at East Devon DC and South Somerset DC (I'm not sure if this is the same individual).
Nicola Bulbeck at Teignbridge BC and Torridge DC
There is a Paul Walker as Chief Executive at Copeland BC in Cumbria, and a Paul Walker as Chief Executive at Hartlepool BC in Cleveland, although those authorities are on opposite sides of the country, so I can't say if these councils are in co-operation at if it is the same Paul Walker.
Peter Latham is Chief Executive at Adur DC and Worthing BC.
Peter Simpson is Chief Executive at Hambleton DC and Richmondshire DC.
Richard Sheard is Chief Executive at South Hams DC and West Devon BC.
Sandy Hopkins is Chief Executive at East Hampshire DC and Havant BC.
Simon Baker is Chief Executive at High Peak BC and Staffordshire Moorlands DC.
Stephen Baker is Chief Executive at Suffolk Coastal DC and Waveney DC.
Sue Smith is Chief Executive at Cherwell DC and South Northamptonshire DC
Terry Huggins is Chief Executive at Breckland and South Holland DC.
West Lumley is Chief Executive at Bolsover DC and North East Derbyshire DC.