  Quantum systems with discrete symmetries can usually be desymmetrized, but
this strategy fails when considering transport in open systems with a symmetry
that maps different openings onto each other. We investigate the joint
probability density of transmission eigenvalues for such systems in
random-matrix theory. In the orthogonal symmetry class we show that the
eigenvalue statistics manifests level repulsion between only every second
transmission eigenvalue. This finds its natural statistical interpretation as a
staggeredsuperposition of two eigenvalue sequences. For a large number of
channels, the statistics for a system with a lead-transposing symmetry
approaches that of a superposition of two uncorrelated sets of eigenvalues as
in systems with a lead-preserving symmetry (which can be desymmetrized). These
predictions are confirmed by numerical computations of the
transmission-eigenvalue spacing distribution for quantum billiards and for the
open kicked rotator.
