But there's no fundamental reason why an engine, or at least an engine family, can't be targeted at both big twins and 4-holers - the PW4000 and CF6 have done pretty well in both markets, for example, even arguably the GEnx.
The PW4000 and CF6-80C2 benefited from a happy coincidence - the requirements for the 767 and 747-400 were nearly identical (and by extension to the A300-600). The available thrust ranges for the 767 went from ~52k to 62k, while the base for the 747-400 was 56k (later increased to about 60k). As a result, the engines were quite literally identical - only the rating plugs need to change to swap between the 747 and the 767 (even the nacelle was common).
The GEnx is shared between the 787 and the 747-8, but the requirements were enough different that the engines are far from identical. Relative to the -1B on the 787, the GEnx-2B on the 747 has a ~7 inch smaller fan, the low compressor (booster in GE lingo) is completely different with one less stage, the LP turbine is completely different, and the gearbox is completely different (to accommodate an IDG instead of the two big starter/generators on the 787) . Only the HP core is common. GE spent a boatload (well into 9 figures) developing the -2B from the -1B.