To do this, you'll need each individual to be easily extractable from their background and be able to place them in to another scene. You will want consistent, even and reproducible lighting, so you will need to shoot with only artificial light in a room with no windows (or at night). Any variations in lighting will make it very obvious that the images were not taken at the same time.
You can either do this with a consistent solid background that can be blended between people or by masking out the background completely (though this can be harder depending on people's hair styles.) The advantage of the first is that it is likely much quicker, but it doesn't allow much of a selection in backdrops. The later is more complicated, but you can use any background shot under similar lighting conditions.
Once you have the individual people, you simply have to arrange them in a way that looks decent. A much easier alternative is to do it as a series of portraits and then use a gallery that places them all next to each other in a nice way. This way, changing them out is much easier and it still looks pretty good (possibly better than a hacked together group photo.)
Also, for 27 people, it is probably easier to just take another group photo when needed than it is to setup the lighting situation and take a highly controlled photo every time they have a new employee.