  Single crystals of Cr$_2$Ge$_2$Te$_6$ were studied by high-resolution
capacitance dilatometry to obtain in-plane ($B\parallel ab$) and out-of-plane
($B\parallel c$) thermal expansion and magnetostriction at temperatures between
2 and 300 K and in magnetic fields up to 15 T. The anomalies in both response
functions lead to the 'magnetoelastic' phase diagrams and separate the
paramagnetic (PM), ferromagnetic low-temperature/low-field (LTF) and aligned
ferromagnetic (FM) phases. The presence of two distinct thermal expansion
anomalies at small fields $B\parallel ab$ of different magnetic field
dependence clearly supports the scenario of an intermediate region separating
PM and LTF phases and is indicative of a tricritical point. Simulations of the
magnetostriction using the Stoner-Wohlfarth model for uniaxial anisotropy
demonstrate that the observed quadratic-in-field behavior in the LTF phase is
in line with a rotation of the spins from the preferred $c$ direction into the
$ab$ plane. Both the LTF and the PM phase close to T$_{\rm C}$ exhibit very
strong pressure dependencies of the magnetization, ${\partial}\ln{M_{\rm
ab}}/{\partial}p_{\rm ab}$, of several hundred %/GPa and also the transition
from the LTF to the FM phase strongly depends on $p_{\rm ab}$ ($\sim
-$280%/GPa), indicating a strong decrease of the uniaxial anisotropy under
applied in-plane pressure. Our data clearly demonstrate the relevance of
critical fluctuations and magnetoelastic coupling in Cr$_2$Ge$_2$Te$_6$.
