Trident
The later version of the trident actually had a fourth engine in a small tail pod just over engine two outlet. Not sure if it was also an apu but it was there for a performance boost. Check out some pics of it and you can see the pod. The idea of thrust apu has been around a long time, heard it suggested in the last few years for a newish aeroplane. All thrust helps with take off but an engine which only works for take off and is then dead weight is inherently inefficient, its just a performance fudge.