  The Mn(Bi$_{1-x}$Sb$_x$)$_2$Te$_4$ series is purported to span from
antiferromagnetic (AF) topological insulator at x = 0 to a trivial AF insulator
at x = 1. Here we report on neutron diffraction and inelastic neutron
scattering studies of the magnetic interactions across this series. All
compounds measured possess ferromagnetic (FM) triangular layers and we find a
crossover from AF to FM interlayer coupling near x = 1 for our samples. The
large spin gap at x = 0 closes rapidly and the average FM exchange interactions
within the triangular layer increase with Sb substitution. Similar to a
previous study of MnBi$_2$Te$_4$, we find severe spectral broadening which
increases dramatically across the compositional series. In addition to
broadening, we observe an additional sharp magnetic excitation in
MnSb$_2$Te$_4$ that may indicate the development of local magnetic modes based
on recent reports of antisite disorder between Mn and Sb sublattices. The
results suggest that both substitutional and antisite disorder contribute
substantially to the magnetism in Mn(Bi$_{1-x}$Sb$_x$)$_2$Te$_4$.
