(This post has not been written completely yet)
Of course the best songs to modify so are those that their scale of chords is an harmonic one in the sense that is a connected arc of chords in the wheel by 4ths.
It is know that in Gypsy Jazz , it is usual to adopt lovely and well known songs to swing Gypsy jazz, usually by extending the major chords X to the X6 version of them (X+ lower relative minor of X), plus use a fast (sometimes 4 times faster than a calm beat ofthe heart) tempo , which gives its dancing swing character.
Now is it possible to have a rather simple rule for such re-harmonizations? The answer is yes,and it is the melodic re-harmonization, which is most often interpolating chords X0 ,X1 X2 between the Chords X -> and Y if Y, X are apart by intervals of 4th or 5th of the original chord progression, so that X=X0->X1=Ybdim->X2=Y or X=X0->X1=Ybbdim->X2=Y , or X=X0->X1->X2=Y etc and X0 X1 (or also X1,X2 in the last case) is a pair of chords in a diatonic scale that their roots are apart by an interval of 3rd . Alternatively if the initial harmony is a scale of chords which is a connected arc in the wheel by 4ths then a rule is to substitute major chords with their lower (or sometimes upper) minor relative chords (thus are a minor 3rd apart therefore a melodic re-harmonization) resulting nevertheless again to a connected arc in the wheel by 4ths. Of course there is also a kind of opposite which is substituting a minor chord with major chord with the same root. This also allows for easier solo improvisation fitting the new melodic re-harmonization of the original chord progression. Now because such chord-relations by intervals of 3rds are relative chords and is called melodic relation of chords we call this re-harmonization melodic re-harmonization. In this minor and major chords alternate with diminished chords as well.
https://www.youtube.com/watch?v=80ZlQ0iTY_g&ab_channel=CoenModder-PianoCouture
https://www.youtube.com/watch?v=T2WV80h3P04&ab_channel=MangoldProject
We may compare this re-harmonization with the chromatic re-harmonization of the post 153 andthe harmonic re-harmonization which is to interpolate between two chords X1->X2 a third chord Y (X1->Y->X2) so that the Y is a 7nth chord in harmonic relation to X2 and resolving to X2 (e.g. if X1=C and X2=G then Y may be Dm7, in total C->Dm7->G . Other example is X1=Am X2=F and then Y=C7 , in total Am->C7->F)
https://www.youtube.com/watch?v=T2WV80h3P04&ab_channel=MangoldProject
We may compare this re-harmonization with the chromatic re-harmonization of the post 153 andthe harmonic re-harmonization which is to interpolate between two chords X1->X2 a third chord Y (X1->Y->X2) so that the Y is a 7nth chord in harmonic relation to X2 and resolving to X2 (e.g. if X1=C and X2=G then Y may be Dm7, in total C->Dm7->G . Other example is X1=Am X2=F and then Y=C7 , in total Am->C7->F)
Of course the best songs to modify so are those that their scale of chords is an harmonic one in the sense that is a connected arc of chords in the wheel by 4ths.
OTHER TYPES OF RE-HARMONIZATION HERE IN JAZZ HERE