Depends what key gets transposed from, e.g. I to V where I = B major then V will be F-sharp major. When transposing I to IV and I is D-flat major, IV will be G-flat major.
Now F-sharp major as tonic, it's less usual than G-flat major but can be found, e.g. Chopin Impromptu no.2. This piece contains a lot of modulation and resulting double-sharps, for example when it modulates to V (C# major) temporarily, e.g. the chord II7 in the key of C# major which is D# major(!) as shown in the first bar of the attached excerpt. Whereas if the piece were nominally in G-flat major, they would be written merely as naturals. Although, i haven't analyzed all of the piece, there are sections where the modulation reduces the number of accidentals.