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In 2015, it was shown that reachability for arbitrary directed graphs can be updated by first-order formulas after inserting or deleting single edges. Later, in 2018, this was extended for changes of size log n/loglog n, where n is the size of the graph. Changes of polylogarithmic size can be handled when also majority quantifiers may be used. In this paper we extend these results by showing that, for changes of polylogarithmic size, first-order update formulas suffice for maintaining (1)arXiv:2004.12739v1 fatcat:ml337i6yhbg6hpok3hbr3d7yym