  We study a class of non-unitary so(2,d) representations (for even values of
d), describing mixed-symmetry partially massless fields which constitute
natural candidates for defining higher-spin singletons of higher order. It is
shown that this class of so(2,d) modules obeys of natural generalisation of a
couple of defining properties of unitary higher-spin singletons. In particular,
we find out that upon restriction to the subalgebra so(2,d-1), these
representations branch onto a sum of modules describing partially massless
fields of various depths. Finally, their tensor product is worked out in the
particular case of d=4, where the appearance of a variety of mixed-symmetry
partially massless fields in this decomposition is observed.
