We present results of a search for anomalous production of two photons together with an electron, muon, $\tau$ lepton, missing transverse energy, or jets using $p\bar{p}$ 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 em