For a system of rigid bodies sharing the same rotation axis: $I_{total}$ = $I_1$ + $I_2$ + $I_3$ + ...

MOI is additive (like mass for translational motion).

Example: Two discs of masses M1, M2 and radii R1, R2 coaxially stacked: $I_{total}$ = M1*$R1^2$/2 + M2*$R2^2$/2

Example: A rod with a disc attached at one end, rotating about the other end of the rod: $I_{total}$ = ($ML^2$/3) + ($mR^2$/2 + m*$L^2$) [parallel axis for disc about rod's end]