There are quite a few advantages. A difficult problem that often arises is blooming of bright areas into adjacent dark areas. So, the overexposed pixels that are in the bright area will leak electrons to adjacent pixels, making them get gray values that are too high. If the contrast is very high, those pixels may be in dark areas. This means that with only two exposures, you'll have to deal with blooming artifacts which shows up as a weak ghosting like effect surrounding bright areas. If you have additional intermediary exposures, the blooming artifacts can be greatly reduced.

Noise is mentioned by Chris in his answer; the more exposures you use, the better the signal to noise ratio will be as the intermediary exposures allow you to use a higher exposure for parts of the image compared to just having two exposures. Also, in the areas where more than one exposure can be used, they can be averaged which reduces the noise more.

Even if you have two images one with more noise than the other, it's still possible to reduce the noise below that of the best of the two by taking a weighted average, the optimal weight when the pictures are normalized to the same brightness and have the same absolute noise, is to take the weights proportional to the square of the exposure. This means that for unnormalized images you should give the images a weight proportional to the exposure.

Another advantage is to have more opportunities to remove changes in the scene that you either don't want to appear in the picture or which could throw off the HDR computations. Suppose that a car with bright lights appears in the scene when you take one of the exposures. Because the bright lights don't appear in the same spot in the other exposures, this will cause artifacts to appear there. If you have more than two exposures you can use another exposure to deal with the affected area.