  We investigate a mechanism of multiple-$q$ states consisting of magnetic
dipole and electric quadrupole degrees of freedom in spin-1 triangular-lattice
systems. By systematically analyzing a minimal effective multipole model with
bilinear multipole-multipole interactions in momentum space on a triangular
lattice, we find minimum conditions of multipole interactions leading to the
multiple-$q$ instability at zero temperature even without single-ion magnetic
anisotropy and higher-order interactions. We present six types of triple-$q$
states with different magnetic dipole and electric quadrupole configurations
depending on the model parameters. Our results indicate that the interplay
between dipole and quadrupole degrees of freedom provides another source of
inducing rich multiple-$q$ states.
