Events with a final state consisting of two or more photons and large missing transverse energy have been observed in e+e- collisions at centre-of-mass energies in the range 192-209 GeV using the OPAL detector at LEP. Cross-section measurements are performed within the kinematic acceptance of the selection and compared with the expectations from the Standard Model process ee -> nu nu gamma gamma (gamma). No evidence for new physics contributions to this final state is observed. Upper limits on sigma(e+e- -> XX) * Br^2(X -> Y gamma) are derived for the case of stable and invisible Y. In the case of massive Y the combined limits obtained from all the data range from 10 fb to 60 fb, while for the special case of massless Y the range is 20 fb to 40 fb. The limits apply to pair production of excited neutrinos (X = nu^*, Y = nu), to neutralino production (X= ~chi_2^0, Y=~chi_1^0) and to supersymmetric models in which X = ~chi_1^0 and Y=~G is a light gravitino.