We study off-shell \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document}-extended Yang-Mills multiplets coupled to conformal supergravity in three spacetime dimensions. Superform formulations are presented for the non-Abelian Chern-Simons actions in the cases \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 1, 2, 3, and the corresponding component actions are explicitly worked out. Such a Chern-Simons action does not exist for \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 4. In the latter case, a superform formulation is given for the BF term that describes the coupling of two Abelian vector multiplets with self-dual and anti-self-dual superfield strengths respectively. The superform results obtained are used to construct linear multiplet action principles in the cases \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 2, 3, 4. The \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 3 and \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 4 actions are demonstrated to be universal in the sense that all known off-shell supergravity-matter systems (with the exception of pure conformal supergravity) may be described using such an action. Starting from the \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 3 and \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 4 Abelian vector multiplets, we also construct composite \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{O}(2) $\end{document} multiplets which are analogues of the four-dimensional construction of an \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 2 reduced chiral scalar engineered from the improved tensor multiplet. Using these composites, we present the superfield equations of motion for \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 3 and \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 4 anti-de Sitter and topologically massive supergravity theories. We also sketch the construction of a large family of higher derivative couplings for \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 3 and \documentclass[12pt]{minimal}
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\begin{document}$ \mathcal{N} $\end{document} = 4 vector multiplets.
