Changing sectional moment of inertia (I) shall change stiffness. But as you change I, bending and torsional stiffness together changes. It is perhaps easier to adjust E, G, mu. Change of E and proportionate adjustment of mu, shall not affect stiffness against torsion. Also note that the axial stiffness is directly proportional to E. You can now think all combinations.
Estimating period of structure, you may assess overall change in system stiffness.