  New reductions for the multicomponent modified Korteveg-de Vries (MMKdV)
equations on the symmetric spaces of {\bf DIII}-type are derived using the
approach based on the reduction group introduced by A.V. Mikhailov. The
relevant inverse scattering problem is studied and reduced to a Riemann-Hilbert
problem. The minimal sets of scattering data $\mathcal{T}_i$, $i=1,2$ which
allow one to reconstruct uniquely both the scattering matrix and the potential
of the Lax operator are defined. The effect of the new reductions on the
hierarchy of Hamiltonian structures of MMKdV and on $\mathcal{T}_i$ are
studied. We illustrate our results by the MMKdV equations related to the
algebra $\mathfrak{g}\simeq so(8)$ and derive several new MMKdV-type equations
using group of reductions isomorphic to ${\mathbb Z}_{2}$, ${\mathbb Z}_{3}$,
${\mathbb Z}_{4}$.
