Double working may be done in certain fruit tree grafts where the scion and understock are incompatible, but the interstock is compatible with both the scion and understock.
In the example, 'Bartlett' pear scions are not compatible with quince understocks. 'Old Home' pear is compatible with both 'Bartlett' and quince and serves as a buffer between the two partners to avoid localized graft incompatiblility.