That's an interesting point about the AVCO-Lycoming geared fan engines used on the BAe 146. Besides the use of four engines when most other comparable commercial jet aircraft used only two, the BAe 146 also had a high wing. However, the 146 was designed for specific applications that favored using four engines and a high wing. Later there was a proposal to develop a twin engine derivative of the aircraft, but it was not built.
The most ubiquitous geared turbofan engine is probably the Garrett TFE731. There were some Dassault Falcon 20 jets that had their GE CF700 turbofan engines replaced with TFE731 geared fan engines. So there is some precedent for this type of engine retrofit. There was also the Lockheed JetStar that used four TFE731 geared fan engines.