Along with the other advice given, don't be afraid to try singing harmony to their melody. The effect will be interesting in the very least. You can decide if you like it or not. I'm trying to imangine how it would sound, and I think it would be good once in a while, if only because everyone sings melody in sing a longs. (not really, but it seems that way)
It could be the new twist that gives you and the band your 15 minutes of fame. It could flop of course, but you find that out by doing.