At LHR the strangest situation must be Lufthansa and soon to be Swiss.
Servisair / Globeground provide above wing services such as check in, Baggage and Dispatch / Load Control whilst Aviance provide the ramp etc.
What makes this unusual ( i believe ) is that the 2 companies are fairly large Handlers who both provide the service that the other supplies, in i may add the same terminal. Aviance give Check in / Loadcontrol & Baggage to Iberia whilst Servisair do the same for Croatian and several others.
Also at Lhr the same situation now applies to Air China who have SGS for check in and Load control but Aviance on the ramp.
There are many examples where The Airline does front of house and handling agents " out back " Gulf Air, Virgin being 2 examples.
They both use Plane Handling on the ramp but PH do not offer passenger Handling facilities