p1= ContourPlot3D[x^4-4*x*y+y^4-16,{x,-3,3},{y,-3,3},{z,3,9},Contours->{0.0},PlotPoints->{100,100,100}]

p2 = ContourPlot3D[z-x^2-y^2,{x,-3,3},{y,-3,3},{z,3,9},Contours->{0.0},PlotPoints->{100,100,100}]

Show[p1,p2]