I have a small list of compositions which have parts which are sung in two different octaves in different versions by singers. The biggest of them is Cetah sri in Dwijavanti (Jujavanti), where Brinda, Mukta and Viswa sing the Navacampaka line in the low octave, while most others sing it in the tara sthayi (I remember one NMN review years ago, where he mentioned that DKJ could not make it to the high point of the song). I obviously don't include instances where singers sing lines in a particular octave because they are not able to manage it where it is to be sung, most commonly seen in the first swaram of the Gowlai pancaratnam (mostly inability) and first swaram of the Sriragam pancatnam (mostly for effect). Some singers are not able to manage some of the higher reaches and rely on the co-singer for that (like Parasala Ponammal on occasion). Some duos produce a harmonic effect by each singing in one octave. But these are not what I mean.
Returning to what I do mean, an example is the last swaram in Endaro mahanubhavulu where it is generally sung as GRR GRR,RR, (higher octave) GRR GRR,RR, (middle octave), whereas KVN for sure sings it GRR GRR,R (higher) R,GRR G RR,R (middle octave), so that the word split comes out right and also the obvious pattern is not sung and the slight asymmetry adds to the effect. [The GRR sounds as though I am angrry, which I'm not!].
The last two examples are from varnams, Natakurinji pada varnam and Kanada ata tala varnam, both at the first swaram of the Anupallavi. There could be more such.