The adaptive mechanisms of homo- and heterosynaptic plasticity play an important role in learning and memory. In order to maintain plasticity-induced changes for longer time scales (up to several days), they have to be consolidated by transferring them from a short-lasting early-phase to a long-lasting late-phase state. The underlying processes of this synaptic consolidation are already well-known for homosynaptic plasticity, however, it is not clear whether the same processes also enable the induction and consolidation of heterosynaptic plasticity. In this study, by extending a generic calcium-based plasticity model with the processes of synaptic consolidation, we show in simulations that indeed heterosynaptic plasticity can be induced and, furthermore, consolidated by the same underlying processes as for homosynaptic plasticity. Furthermore, we show that by local diffusion processes the heterosynaptic effect can be restricted to a few synapses neighboring the homosynaptically changed ones. Taken together, this generic model reproduces many experimental results of synaptic tagging and consolidation, provides several predictions for heterosynaptic induction and consolidation, and yields insights into the complex interactions between homo- and heterosynaptic plasticity over a broad variety of time (minutes to days) and spatial scales (several micrometers).