>Coaxial-rotor helicopters have one big advantage compared to single-rotor helicopters and that is that they can lift a lot more

Coaxial helicopters have only one advantage in respect to conventional helicopters and that is compactness.

Indeed, stacking two rotor one above the other, means that:
* the tail rotor is no more required and;
* the rotor diameter can be more or less reduced.

Anyway:
1.  a horizontal tailplane (and the relevant tailboom) is still needed for stability, so you don't really get rid of the whole tailboom;
2. diameter of the rotor cannot be reduced too much before running into performance degradations;
3. aerodynamic interferences between the rotors make the lower rotor loose some 10 to 15% efficiency (but in a conventional helicopter the tail rotor eat some 10 to 15% of the power available so let's call it even);
4. rotor head becomes packed with rods and other rotating mechanisms increasing the total aerodynamic drag;
5. for sure I'm missing something.

For all these reasons a coaxial design is really important where compactness is at a premium. Packing more rotors one on top of the other will only worsen everything, especially points 3. and 4., without bringing any improvement.