  We study multipole decompositions of the electromagnetic currents of
spin-1/2, 1, and 3/2 particles described in terms of Lagrangians designed to
reproduce representation specific wave equations which are second order in the
momenta and which emerge within the recently elaborated Poincar\'e covariant
projector method. We calculate the electric multipoles of the above spins for
the spinor, the four-vector, and the four-vector--spinor representations,
attend to the most general non-Lagrangian spin-3/2 currents which are allowed
by Lorentz invariance to be of third order in the momenta and construct the
linear current equivalent of identical multipole moments of one of them. We
conclude that such non-Lagrangian currents are not necessarily more general
than the two-term currents emerging within the covariant projector method. We
compare our results with those of the conventional Proca-, and Rarita-Schwinger
frameworks. Finally, we test the representation dependence of the multipoles by
placing spin-1 and spin-3/2 in the respective (1,0)$\oplus$(0,1), and
(3/2,0)$\oplus$(0,3/2) single-spin representations. We observe representation
independence of the charge monopoles and the magnetic dipoles, in contrast to
the higher multipoles, which turn out to be representation dependent. In
particular, we find the bi-vector $(1,0)\oplus (0,1)$ to be characterized by an
electric quadrupole moment of opposite sign to the one found in $(1/2,1/2)$,
and consequently, to the $W$ boson. Our finding points toward the possibility
that the $\rho$ meson could transform as part of an antisymmetric tensor with
an $a_{1}$ meson-like state as its representation companion.
