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$_3$.
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