Ok, there is a 3TNE84T which is the turbo version of the 4310's engine (I don't see a similar version of the 4410's 3TNE88...)
3TNE84
Number of cylinders: 3
Bore x stroke mm: 84 x 90
Industrial horsepower: 33.0 hp @ 3000 rpm
Generator horsepower: 19.8 hp @ 1800 rpm
Displacement cc: 1496
Dry weight, recoil start (electric) kg: 138/155
3TNE84T
Number of cylinders: 3
Bore x stroke mm: 84 x 90
Industrial horsepower: 41.4 hp @ 3000 rpm
Generator horsepower: 25.2 hp @1800 rpm
Displacement cc: 1496
Dry weight, recoil start (electric) kg: 142/160
Note: the yardstick moves! The performance boost is greater than it first looks, since the scale is moved on these charts...
It is used in marine generators (Kohler) and construction equipment (Yanmar's V4-3 mini-wheel loader )
I saw a price of $2400, but am not sure if that will make an 3TNE84 an 3TNE84T... I am checking...