  In the present work, magnetic properties of single crystal
(Fe$_{1-x}$Mn$_x$)$_2$Mo$_3$O$_8$ ($0<x<1$) have been studied by performing
extensive measurements. A detailed magnetic phase diagram is built up, in which
antiferromagnetic state dominates for $x<0.25$ and ferrimagnetic phase arises
for $x>0.3$. Meanwhile, sizeable electric polarization of spin origin is
commonly observed in all samples, no matter what the magnetic state is. For the
samples hosting a ferrimagnetic state, square-like magnetic hysteresis loops
are revealed, while the remnant magnetization and coercive field can be tuned
drastically by simply varying the Mn-content or temperature. Possible
coexistence of the antiferromagnetic and ferrimagnetic phases is proposed to be
responsible for the remarkable modulation of magnetic properties in the
samples.
