The proposed 3000 - 4000 shp RR turboprop was the RB.510. At one point there was a proposal for a 748 successor using a pair of those engines on a new wing mated to mostly-a-146 fuselage.
Fokker were apparently also interested in it for the F.27 successor but had to scale-back to what became the F.50 when Rolls dropped the engine, presumably around 1983, constraining their choice to the PW12_. Odd that they didn't go with the T64 which sat in exactly the same powerband as the RR proposal, but perhaps the economics didn't work.
RR now also own Continental, which explains a Cessna 150 I saw the other day with R/R decals on the engine hood!