relying on the Time Warp (optimistic) synchronization protocol already allow for exploiting parallelism, several techniques have been proposed to further favor performance. Among them we can mention optimized approaches for state restore, as well as techniques for load balancing or (dynamically) controlling the speculation degree, the latter being specifically targeted at reducing the incidence of causality errors leading to waste of computation. However, in state of the art Time Warp systems, events' processing is not preemptable, which may prevent the possibility to promptly react to the injection of higher priority (say lower timestamp) events. Delaying the processing of these events may, in turn, give rise to higher incidence of incorrect speculation. In this article we present the design and realization of a fine-grain time-sharing Time Warp system, to be run on multi-core Linux machines, which makes systematic use of event preemption in order to dynamically reassign the CPU to higher priority events/tasks. Our proposal is based on a truly dual mode execution, application vs platform, which includes a timer-interrupt based support for bringing control back to platform mode for possible CPU reassignment according to very fine grain periods. The latter facility is offered by an ad-hoc timer-interrupt management module for Linux, which we release, together with the overall time-sharing support, within the open source ROOT-Sim platform. An experimental assessment based on the classical PHOLD benchmark and two real world models is presented, which shows how our proposal effectively leads to the reduction of the incidence of causality errors, as compared to traditional Time Warp, especially when running with higher degrees of parallelism.