The authors add one more parameter to a bibasic indefinite sum which Gasper found earlier. While series whose partial sums can be found exactly are rare, and are easy to prove once found, the interesting ones are far from easy to find. As the authors show in this paper, they can be surprising useful. One application is to the transformation of a very well poised \(_{10}\phi_ 9\) on base \(q^ 2\) to another very well poised \(_{10}\phi_ 9\) on base q plus a ratio of infinite products. Other strange but interesting transformations are given, including one series which has terms on base \(q^ k\), \(k=1,2,3,4,5\) on one side and \(q^ 4\) on the other.