  We propose a new drag phenomenon, an interband magnon drag, and report on
interaction effects and multiband effects in magnon transport of ferrimagnetic
insulators. We study a spin-Seebeck coefficient $S_{\textrm{m}}$, a magnon
conductivity $\sigma_{\textrm{m}}$, and a magnon thermal conductivity
$\kappa_{\textrm{m}}$ of interacting magnons for a minimal model of
ferrimagnetic insulators using a $1/S$ expansion of the Holstein-Primakoff
method, the linear-response theory, and a method of Green's functions. We show
that the interband magnon drag enhances $\sigma_{\textrm{m}}$ and reduces
$\kappa_{\textrm{m}}$, whereas its total effects on $S_{\textrm{m}}$ are small.
This drag results from the interband momentum transfer induced by the
magnon-magnon interactions. We also show that the higher-energy band magnons
contribute to $S_{\textrm{m}}$, $\sigma_{\textrm{m}}$, and
$\kappa_{\textrm{m}}$ even for temperatures smaller than the energy difference
between the two bands.
