Actually, the lift would reduce, and the power needed would rise noticibly if you added an extra blade onto most helicopters. The total thrust (lift) that could be produced would be theoretically greater, if you pulled the helo into a stall condition, but in normal hover and forward flight, the extra blade would actually cost you performance Why?
1) The blade would give you too much area, so that the net angle of attack would drop, and the blades would operate below best efficiency
2) The extra blade and its attachment hardware, and the extra meat on the swashplate all weigh more, so that it robs payload.
3) The extra blade has its own parasite drag, so it eats engine power just to spin it around, while not producing any more lift (except near stall, a long way away from normal flight).
That doesn't mean that 3 blades is worse than 2 blades, it means that when a helo is designed for 2 blades adding an extra blade is worse than leaving things alone. In fact, if you removed a blade from most helicopters, the hover performance would go up (the lift per horsepower would increase). But because you had less blade area, you would encounter stall earlier, at lower speed and lower altitude, so that speed and range would suffer.