A number of general trends are known to occur in systems displaying secondary processes in glasses and glass formers. Universal features can be identified as components of large and small cooperativeness whose competition leads to excess wings or apart peaks in the susceptibility spectrum. To the aim of understanding such rich and complex phenomenology we analyze the behavior of a model combining two apart glassy components with a tunable different cooperativeness. The model salient feature is, indeed, based on the competition of the energetic contribution of groups of dynamically relevant variables, e.g., density fluctuations, interacting in small and large sets. We investigate how the model is able to reproduce the secondary processes physics without further ad hoc ingredients, displaying known trends and properties under cooling or pressing.
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