cow = ExampleData[{"Geometry3D", "Cow"}]; Manipulate[cow /. GraphicsComplex[array1_, rest___] :> GraphicsComplex[(# (Norm[#]^-coeff)) & /@ array1, rest], {{coeff, .25}, 0, 1}] 
Edit
To answer to Clément's comment, here is same thing with constant plot range :
cow = ExampleData[{"Geometry3D", "Cow"}]; Manipulate[cow /. GraphicsComplex[array1_, rest___] :> GraphicsComplex[(# (Norm[#]^-coeff)) & /@ array1, rest], {{coeff, .25}, 0, 1}]
cow = ExampleData[{"Geometry3D", "Cow"}]; Manipulate[cow /. GraphicsComplex[array1_, rest___] :> GraphicsComplex[(# (Norm[#]^-coeff)) & /@ array1, rest], {{coeff, .25}, 0, 1}]
Edit
To answer to Clément's comment, here is same thing with constant plot range :
cow = ExampleData[{"Geometry3D", "Cow"}]; Manipulate[ cowManipulate[cow /. GraphicsComplex[array1_, rest___] :> rest___] :> (GraphicsComplex[ Map[# GraphicsComplex[(Norm[#]^# (Norm[#]^-coeff)) &, array1,/@ {1}]array1, rest]), {{coeff, .25}, 0, 1}]
cow = ExampleData[{"Geometry3D", "Cow"}]; Manipulate[ cow /. GraphicsComplex[array1_, rest___] :> (GraphicsComplex[ Map[# (Norm[#]^(-coeff)) &, array1, {1}], rest]), {{coeff, .25}, 0, 1}]
cow = ExampleData[{"Geometry3D", "Cow"}]; Manipulate[cow /. GraphicsComplex[array1_, rest___] :> GraphicsComplex[(# (Norm[#]^-coeff)) & /@ array1, rest], {{coeff, .25}, 0, 1}]