North Yorkshire doesn't have a multi-operator ticket; technically, Explorer NE is valid on services around Richmond and Whitby but whilst it is valid on some operators, it's only Arriva NE on which it's valid there. Explorer NE is valid on Go Ahead, Arriva and Stagecoach as well as Travelsure (plus some trains, Shields Ferry and Metro) and that covers most of Northumberland and Teesside buses. However, the retrenchment of Arriva in Co Durham means there are substantial tracts of territory that are mainly Scarlet Band or Weardale on which it isn't valid.
In the South West, Dorset doesn't have a multi-operator ticket and neither does Somerset. Gloucestershire doesn't any more though it truly never did. The Cotswold Explorer was valid on certain Stagecoach and Johnsons services as well as Swanbrook and Pulhams but those latter two have now pulled out. Herefordshire doesn't have a one though woeful Worcestershire does.