Answer
This is not possible.
Work Step by Step
The moment of inertia of an object increases as mass is moved to be farther from the axis of rotation.
For a cylindrical object of radius R, rotated around its axis of symmetry, the moment of inertia is maximized when all of the mass is as far from the axis as possible, i.e., at the rim. With all of the mass at the rim (or as close as possible), the moment of inertia is exactly $MR^2$; it cannot be greater without having mass at a distance greater than R.
