  It is an open problem whether any pair of Bessel sequences with wavelet
structure can be extended to a pair of dual frames by adding a pair of singly
generated wavelet systems. We consider the particular case where the given
wavelet systems are generated by the multiscale setup with trigonometric masks
and provide a positive answer under extra assumptions. We also identify a
number of conditions that are necessary for the extension to dual multiscale
wavelet frames with any number of generators, and show that they imply that an
extension with two pairs of wavelet systems is possible. Along the way we
provide examples showing that extensions to dual frame pairs are attractive
because they often allow better properties than the more popular extensions to
tight frames.
