  We present a combined study of zero-field $^{51}$V and $^{127}$I NMR at
ambient pressure and specific heat and magnetization measurements under
pressure up to 2.08 GPa on bulk single crystals of the van-der-Waals
ferromagnet VI$_3$. At ambient pressure, our results consistently demonstrate
that VI$_3$ undergoes a structural transition at $T_s \approx $78 K, followed
by two subsequent ferromagnetic transitions at $T_{FM1} \approx $50 K and
$T_{FM2} \approx $36 K upon cooling. At lowest temperature ($T < T_{FM2}$), two
magnetically-ordered V sites exist, whereas only one magnetically-ordered V
site is observed for $T_{FM1} < T\,< T_{FM2}$. Whereas $T_{FM1}$ is almost
unaffected by external pressure, $T_{FM2}$ is highly responsive to pressure and
merges with the $T_{FM1}$ line at $p \approx 0.6 $GPa. At even higher pressures
($p \approx $1.25\,GPa), the $T_{FM2}$ line merges with the structural
transition at $T_s$ which becomes moderately suppressed with $p$ for $p < 1.25$
GPa. Taken together, our data point towards a complex magnetic structure and an
interesting interplay of magnetic and structural degrees of freedom in VI$_3$.
