  The complete magnetic and multiferroic phase diagram of
Mn$_{1-x}$Co$_{x}$WO$_4$ single crystals is investigated by means of magnetic,
heat capacity, and polarization experiments. We show that the ferroelectric
polarization $\overrightarrow{P}$ in the multiferroic state abruptly changes
its direction twice upon increasing Co content, x. At x$_{c1}$=0.075,
$\overrightarrow{P}$ rotates from the $b-$axis into the $a-c$ plane and at
x$_{c2}$=0.15 it flips back to the $b-$axis. The origin of the multiple
polarization flops is identified as an effect of the Co anisotropy on the
orientation and shape of the spin helix leading to thermodynamic instabilities
caused by the decrease of the magnitude of the polarization in the
corresponding phases. A qualitative description of the ferroelectric
polarization is derived by taking into account the intrachain ($c-$axis) as
well as the interchain ($a-$axis) exchange pathways connecting the magnetic
ions. In a narrow Co concentration range (0.1$\leq$x$\leq$0.15), an
intermediate phase, sandwiched between the collinear high-temperature and the
helical low-temperature phases, is discovered. The new phase exhibits a
collinear and commensurate spin modulation similar to the low-temperature
magnetic structure of MnWO$_4$.
