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Railway timetables are planned periodically, but operational planners continuously need to deviate from this base: extra trains are added, or infrastructure changes are made, requiring local updates to the existing schedule. We study this process as a sequential extra train scheduling problem, in which requests arrive one at a time and must be routed and timed against the existing timetable while minimising deviation from it. Commonly, each admitted train is fixed before the next request arrives, and all accumulated solver knowledge is discarded between calls. We propose an incremental MaxSAT framework over Integer Difference Logic (MaxSMT) that retains accumulated solver state across successive extra-train additions, rather than solving from scratch after each request. We evaluate the approach on the Rhätische Bahn network using different solving strategies and compare against a MIP baseline. Retained solver state substantially reduces solve time for successive additions, increasingly so as more extra trains are admitted, and is an order of magnitude faster than MIP given the same setup. Beyond solving time, we show that jointly re-optimising over all admitted extra trains yields better cumulative objective values, and that our approach achieves this while prioritising adjustments in the timetable region affected by the new request.