screening classical gravity

Can you modify the Lagrange-density \(\mathcal{L}(\Phi,\nabla\Phi) = (\nabla\Phi)^2/2-4\pi G\rho\Phi\) of classical gravity to introduce a screening-mechanism? Would it be possible to do the same thing in electrodynamics \(\mathcal{L} = F_{\mu\nu}F^{\mu\nu}/4 + 4\pi/c\:A_\mu\jmath^\mu\)?