Currently grip control during in-hand manipulation is usually modeled as part of a monolithic task, yielding complex controllers based on force control specialized for their situations. Such non-modular and specialized control approaches render the generalization of these controllers to new in-hand manipulation tasks difficult. Clearly, a grip control approach that generalizes well between several tasks would be preferable. We propose a modular approach where each finger is controlled by an independent tactile grip controller. Using signals from the human-inspired biotac sensor, we can predict future slip - and prevent it by appropriate motor actions. This slip-preventing grip controller is first developed and trained during a single-finger stabilization task. Subsequently, we show that several independent slip-preventing grip controllers can be employed together without any form of central communication. The resulting approach works for two, three, four and five finger grip stabilization control. Such a modular grip control approach has the potential to generalize across a large variety of inhand manipulation tasks, including grip change, finger gaiting, between-hands object transfer, and across multiple objects.