  In this study, we explore multiple higher-order pole solutions in spinor
Bose--Einstein condensates. These solutions are associated with different pairs
of higher-order poles of the transmission coefficient in the inverse scattering
transform, and they represent solutions of the spin-1 Gross--Pitaevskii
equation. We introduce a direct scattering map that maps initial data to
scattering data, which includes discrete spectrums, reflection coefficients,
and a polynomial that replaces normalization constants. To analyze symmetries
and discrete spectrums in the direct problem, we introduce a generalized cross
product in 4-dimensional vector space. Additionally, we characterize the
inverse problem in terms of a $4\times 4$ matrix Riemann--Hilbert problem that
is subject to residue conditions at these higher-order poles. In the
reflectionless scenario, the Riemann--Hilbert problem can be converted into a
linear algebraic system. The resulting algebraic system has a unique solution,
which allows us to display multiple higher-order poles solutions.
