Hey Adam, It is not possible to change the exposure with anything but the three. You can ‘aid’ them with additional light sources – even then, the exposure is controlled ONLY by the shutter, aperture and ISO.
Both the exposure compensation (EC) and the bracketing are technics where you ‘instruct’ the camera to read a particular frame in a particular way. Let me take an example: If you want the image to be more bright, you set a positive EC, and a negative one for slightly darker image. Now, this just tells the camera that you want a brighter/darker (than normal, indicated by zero compensation) image. HOW this is achieved, is ONLY by altering the parameters of the exposure triangle. As the name goes, the value is just a compensation for light that the camera reads.
Hope it helps!
PS.: The exposure compensation doesn’t work in the FULL MANUAL mode : works only in shutter/aperture priority and other semi-auto modes.. If I was clear in my explanation, you should be able to get the reason ;) Try.