The amount of illumination increases as you add more strobes, but not linearly. The point of diminishing returns is, basically, right away. This is because flash power is proportional to the square of the guide number. Or to look at it the other way around, the guide number is related to the square root of the flash power. Why all these powers and roots? It's the inverse square law in action.
Practically speaking, this means that when you add another flash, the resulting guide number is the square root of the sum of the squares of the guide numbers of each individual flash.
For example, if you have two flashes with guide numbers of 36, the resulting guide number is about 51:
sqrt(36²+36²) = 50.91...
Or, if you mix a relatively powerful flash with GN 50 with a little GN 20 unit, you get a very unimpressive-sounding increase:
sqrt(50²+20²) = 53.85...
It logically follows that if you want to double flash power, you need four of the same flashes. For example, with some hard numbers:
sqrt(36²×4) = 72
So, basically: increased power gets expensive quickly. This is true whether increasing the power of a single flash or adding in a second — the math is the same. To increase the guide number — the distance to which you can cast a useful amount of light — by a small amount requires an ever-increasing amount of additional power.
The main advantage of multiple flash units is the ability to shape light and shadow. That little GN 20 flash might not add much sheer brightness, but it could soften shadows or add a sparkle to someone's eyes.