Mostly no.......
More mass and less stiffness ultimately leads to collapse.
Unless you can find the (unobtainable) building material of infinite stiffness, any structure will have an intrinsic period of oscillation.
The trick is to make that period so different from likely inputs that feedback cannot develope..
Check out the CitiBank Tower in N.Y.C.
They had to install a damper to make that one work.