Getting upgraded as an entire group is almost impossible. However, getting upgraded as a single passenger isn't as hard as it seems. Book your ticket separately, if you don't mind being separated from the group, and give yourself a better chance.
Book a Full Plane
An airline would rather upgrade a few customers than lose their business entirely.
Avoid Business Hours
Less "fancy" business people=more room in first class
Travel on an Empty Flighty
For an empty flight, there may be a weight balance issue. Because of this, staff will have to move certain people to business or first class.