Remember that the white background is a light source. As it gets brighter it will overpower the sensor and cause clipping. That's not necessarily bad, but it has to be controlled relative to the subject.
A good rule of thumb to use as a starting point is the one Zack points out; set the background lighting, then read it as a light source from the back of the subject. He suggests having it read the same as the main light. This helps to determine how far from the background the subject has to be. If the background lights read F16, then to get the background (as a light source) to read F8 the subject will have to be farther away than if the background lights read F11.
F8 for the subject and F11 for the background may not result in white. If its necessary to set the background at F16 then the only option is to increase the exposure on the subject the same one stop more or get them farther from the background.


