• Is the flavor pattern of the non-MFV new physics related to the standard model flavor pattern or not? Having these questions in mind, we focus in this work on supersymmetric (SUSY) mod- els with a hybrid gauge- and gravity-mediation of supersymmetry breaking [6]. Gauge- mediation is well motivated since it solves the flavor problem of generic supersymmetric models. It should be kept in mind, however, that, in principle, gravity-mediated contribu- tions are unavoidable. What is called pure gauge-mediation has an implicit assumption that the gravity-mediated contributions are quantitatively negligible. Indeed, this is the case if the source of supersymmetry breaking are F -terms with scales that are many orders of magnitude below ( m$_{Z}$m$_{Pl}$ ). Pure gauge-mediation, if realized in Nature, will not provide us with additional data to try and understand the standard model flavor puzzle, namely the physics that leads to the structure observed in the Yukawa sector. In contrast, in the framework called hybrid gauge- and gravity-mediation , there is an F - term within a few orders of magnitude below ( m$_{Z}$m$_{Pl}$ ). This class of models provides an example of a well-motivated theoretical framework where the dominant flavor structure of the new physics (the soft supersymmetry breaking parameters) is MFV, coming from gauge- mediation, but there are sub-dominant contributions, from gravity-mediation, that are non- MFV and that lead to potentially observable deviations in precision flavor measurements. In a previous work [7], we assumed that the structure of the non-MFV terms is related to that of the Yukawa couplings. Specifically, we assumed that there is an approximate Froggatt-Nielsen (FN) symmetry [8] that leads to selection rules which, in turn, dictate the structure of both the Yukawa couplings and the soft supersymmetry breaking terms [9, 10]. In this work, in order to further explore the questions formulated above, we take a different path, where the structure of non-MFV terms is not related to the standard model one. Specifically, we assume that the gravity-mediated contributions to the squark masses- squared are anarchical, namely they are all of the same order, with no special features. Such unrelated structures might arise because the Yukawa couplings come from the su- perpotential, while the soft masses-squared come from the Kahler potential. The two sec- tors may have different dynamics, or different selection rules from approximate symmetries. Model building directions are suggested by the framework of Ref. [11] that involves a strongly coupled sector, which is approximately conformally invariant and leads to large anomalous 3