The change of key signature from C# major to Db major (enharmonic keys) is not a modulation (modulation is about the music).From a Twitter handle called "Threatening Musical Notation", modulating from A major to C# major to Db major:
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One would need a compelling reason for this to be useful (and not pure sadism). One possible valid reason would if the music modulates further towards the "sharp" side, for example to Ab major.