Hierarchy of supersymmetric higher spin connections

We focus on the geometrical reformulation of free higher spin supermultiplets in $4D,~\mathcal{N}=1$ flat superspace. We find that there is a de Wit-Freedman like hierarchy of superconnections with simple gauge transformations. The requirement for sensible free equations of motion imposes constraints on the gauge parameter superfields. Unlike the non-supersymmetric case there is no unique way of doing that and thus generating many different but, on-shell equivalent, constrained descriptions of the same physical system. By lifting the constraints non-geometrically we find that all known descriptions of integer and half-integer supermultiplets are produced by the different ways of decoupling higher order superconnections. Also we find that there exist a consistent constrained description of half-integer supermultiplets which can not be lifted to an unconstrained formulation. In the constrained formulation, the various descriptions can be labeled as geometrical or non-geometrical if the equations of motion can be expressed only in terms of superconnections or not.