We present results of a search for anomalous production of two photons together with an electron, muon, τ lepton, missing transverse energy, or jets using pp collision data from 1.1–2.0  fb−1 of integrated luminosity collected by the Collider Detector at Fermilab (CDF). The event yields and kinematic distributions are examined for signs of new physics without favoring a specific model of new physics. The results are consistent with the standard model expectations. The search employs several new analysis techniques that significantly reduce instrumental backgrounds in channels with an electron and missing transverse energy.