  In the article arXiv:1108.5443 we established a general group-theoretical
approach to the construction of B\"acklund transformations. We then showed how
this construction can be applied to construct B\"acklund transformation between
equations which are Darboux integrable. Here we give a number of detailed
examples and new applications which demonstrate the theory. In particular our
final example demonstrates how our group theoretical approach produces all the
B\"acklund transformations in arXiv:0707.4408. We also prove, using group
methods, a non-existence theorem for B\"acklund transformatons which disagrees
with part 2 of Theorem 1 in arXiv:0707.4408.
