  This paper considers Darboux transformations of a bispectral operator which
preserve its bispectrality. A sufficient condition for this to occur is given,
and applied to the case of generalized Airy operators of arbitrary order $r>1$.
As a result, the bispectrality of a large family of algebras of rank $r$ is
demonstrated. An involution on these algebras is exhibited which exchanges the
role of spatial and spectral parameters, generalizing Wilson's rank one
bispectral involution. Spectral geometry and the relationship to the Sato
grassmannian are discussed.
