  The off-shell actions for $\cal N$-extended conformal supergravity theories
in three dimensions were formulated in [1,2] for $1\leq {\cal N} \leq 6$ using
a universal approach. Each action is generated by a closed super three-form
which is constructed in terms of the constrained geometry of $\cal N$-extended
conformal superspace. In this paper we initiate a program to recast these
actions (and to formulate their higher-spin counterparts) in terms of
unconstrained gauge prepotentials as integrals over the full superspace. We
derive transverse projection operators in $\cal N$-extended Minkowski
superspace and then use them to construct linearised rank-$n$ super-Cotton
tensors and off-shell $\cal N$-extended superconformal actions. We also propose
off-shell gauge-invariant actions to describe massive higher-spin
supermultiplets in $\cal N$-extended supersymmetry. Our analysis leads to
general expressions for identically conserved higher-spin current multiplets in
$\cal N$-extended supersymmetry.
