It's possible. You've seen it and it looks fine to you.

You shouldn't because the key light is seen by your eye as
the light source. For example, you have Bob and Mary
sitting at a table in a kitchen. The light is coming in through
the window which is at Bob's back. So your key light is the
coming in through the window. You shoot Mary's face over
Bob's shoulder - light by the key light (coming in from the
window). Then you move the camera to shoot Bob's face
over Mary's shoulder so you decide to move the key light. Now
the light isn't coming in from the window it's coming from
somewhere behind Mary. Sure, Bob's face is just as well lit as
Mary's was, but your audience notices.

So you keep the fill (or source) light is it is behind Bob's back.
Now Bob does not need to be totally backlit with his face in
darkness - it wouldn't be if you were sitting in a real room with
him. So you add some light to Bob's face and even reduce the
key light so you get a pleasing shot.

If your style is to move the key light, you should do it. You
should set up a scene (like Bob and Mary sitting at a table
in a kitchen) and try several methods of lighting. That way
you will find what works best for you and your style.

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The aim of an argument or discussion should not be victory, but progress.
Joseph Joubert, essayist (1754-1824)

Thanks for the reply!
I was also wondering if it was possible to have two key lights around the set, or is it only ever possible to have one, and then everything else is considered a fill. (So, in your example, the light used for Bobs face would be a fill, and not as strong as the key.)

The "key" light should be considered the source light. For
example; on a day exterior the source is the sun - a night
exterior in the desert it's the moon. A night exterior on a city
street will have several sources of light. A small motel room with
one lamp will have one source of light - a living room in a large
house might have three or four lamps so there will more sources of
light.

What you want to do when lighting a scene is decide what where the
light is coming from (if there was no camera or crew in there) and
light accordingly. Bob and Mary sitting in the kitchen in the
morning with no lights on will have only one source of light - the
sun streaming in the window. So you have one key light. Then you
use more lights to simulate what our eyes would see that the
camera cannot. A light used to reduce the shadow on Bob's face
would be called a "fill" and not the "key".

But it is possible to have two key lights. If it's a night
interior in a room lit by two lamps, you might use two "key"
lights.

Not long ago, there was a discussion thread here, where someone argued about using 'organic' lighting, i.e. using just whatever light is available. He framed the argument from an angle of getting the most natural look, what our eyes see, and not something lit by dozens of reflectors, bounce boards, through cookies, gels, filters, etc.

Unfortunately, such argument fails due to the significant difference between a human eyes and a camera sensor and lens. Such organic lighting would work just fine if cameras had sensors as sensitive as the retina of the human eye; not to mention the dynamic range. Since they don't (the difference in sensitivity, and especially in dynamic range, is huge), we must use light to compensate for such significant shortcomings.

Basic rule requires that the light in a scene be consistent. Unless there is a very specific dramatic reason to break such a rule, your goal is to light your set the way it would be lit naturally, making sure enough light is there for camera to see everything properly. Then, you fill the areas that cannot be seen by the camera until they are all properly visible. You make sure that everything that needs to be seen can be seen properly from all angles you plan to use.

Beyond that, light is a very creative artistic tool, which can add significant artistic quality to the image, when applied by a gifted craftsman. For this, you need talent and experience, although there are many books that get into this matter.

Thanks for the responses!
Vasic- are there any books in particular on the subject of lighting that you would recommend?