We elaborate on the structure of higher-spin mathcal{N} = 2 supercurrent multiplets in four dimensions. It is shown that associated with every conformal supercurrent {J}_{alpha (m)overset{cdot }{alpha }(n)} (with m, n non-negative integers) is a descendant {J}_{alpha left(m+1right)overset{cdot }{alpha}left(n+1right)}^{ij} with the following properties: (a) it is a linear multiplet with respect to its SU(2) indices, that is {D}_{beta}^{Big(i}{J}_{alpha left(m+1right)overset{cdot }{alpha}left(n+1right)}^{jkBig)}=0 and {overline{D}}_{dot{beta}}^{Big(i}{J}_{alpha left(m+1right)overset{cdot }{alpha}left(n+1right)}^{jkBig)}=0 ; and (b) it is conserved, {partial}^{beta overset{cdot }{beta }}{J}_{beta alpha (m)overset{cdot }{beta}overset{cdot }{alpha }(n)}^{ij}=0 . Realisations of the conformal supercurrents {J}_{alpha (s)overset{cdot }{alpha }(s)} , with s = 0, 1, …, are naturally provided by a massless hypermultiplet and a vector multiplet. It turns out that such supercurrents and their linear descendants {J}_{alpha left(s+1right)overset{cdot }{alpha}left(s+1right)}^{ij} do not occur in the harmonic-superspace framework recently described by Buchbinder, Ivanov and Zaigraev. Making use of a massive hypermultiplet, we derive non-conformal higher-spin mathcal{N} = 2 supercurrent multiplets. Additionally, we derive the higher symmetries of the kinetic operators for both a massive and massless hypermultiplet. Building on this analysis, we sketch the construction of higher-derivative gauge transformations for the off-shell arctic multiplet Υ(1), which are expected to be vital in the framework of consistent interactions between Υ(1) and superconformal higher-spin gauge multiplets.