The coupling of spin-3 gauge fields to three-dimensional Maxwell and AdS-Lorentz gravity theories is presented. After showing how the usual spin-3 extensions of the Ad S and the Poincare algebras in three dimensions can be obtained as expansions of sl (3, R) algebra, the procedure is generalized so as to define new higher-spin symmetries. Remarkably, the spin-3 extension of the Maxwell symmetry allows one to introduce a novel gravity model coupled to higher-spin topological matter with vanishing cosmological constant, which in turn corresponds to a flat limit of the AdS-Lorentz case. We extend our results to define two different families of higher-spin extensions of three-dimensional Einstein gravity. (C) 2018 The Authors. Published by Elsevier B.V.