The danger in using natural light (or a single key light) plus reflector fill is that the background can be neglected, so that the subjects appear in a sort of muddy limbo. Since our ground rules deny us extra lights for the walls, we'll need other strategies.
One approach is to use those other two pieces of foamcore in your inventory. Build aluminum reflectors with them, position then near the talent-filling reflector, and rake their light across the background. Often, this is all you'll need.
If that doesn't work (and if the window or other key light position permits), move everything closer to the background. Many times, you will increase spill light on the BG enough to do the job.
And if that won't work, go the opposite way by moving the background closer to the subjects. In an office environment, you can often liberate pieces of Dilbert cube walls and prop them up behind the subject. In a classroom, a rolling chalk or bulleting board can be wheeled into place. Or if the environment is not that important, a strategic drape behind the talent will often do the job.
Good shooting!
Contributing Editor Jim Stinson is the author of the book Video Communication and Production.
You can now buy those familiar blue plastic tarpaulins with one side colored soft silver. In 5x8 to maybe 8x12-foot sizes, these make very soft, ultra-large reflectors.
Hang them from grid ceilings by their grommet edges or mount them on pairs of century stands to create entire walls of soft bounce light. Often, this will let you key directly with your spotlight, rather than by combining it with a soft box or umbrella. Hung opposite the key, the huge silver wall can bounce back a wonderful "window light" fill.
A word of caution: because these reflectors are clumsy and hard to adjust, use them when you have plenty of setup time to experiment with your key and reflector positions.


3 Point Lighting
Light it Right (DVD)
Video Lighting (DVD)
Video Lighting Tips (DVD)
One Light Wonder
Three-Point Lighting 101
Book of Forms - Lighting Plot
Creating Shadows
Depth of Field
Producing a Documentary Part 1