  Using multiple q-integrals and a determinant evaluation, we establish a
multivariable extension of Bailey's nonterminating 10-phi-9 transformation.
  From this result, we deduce new multivariable terminating 10-phi-9
transformations, 8-phi-7 summations and other identities. We also use similar
methods to derive new multivariable 1-psi-1 summations. Some of our results are
extended to the case of elliptic hypergeometric series.
