This morning I saw the person holding the sefer Torah at the Bimah during Hoshanos pass the Torah to another person for a short time so he could walk around the Bimah with his lulav and Esrog.
I never saw such behavior in the past; the sefer Torah holder simply did not walk around during Hoshanos since he was preoccupied with another minhag / mitzva of holding the Torah during Hoashanos.
I would expect that passing the Torah to another might even be prohibited because of "ain ma'avirin al hamitzvos" one may not pass over a mitzva that is closer and certainly not one which one is actively involved. (See Kesef Mishna Hilchos Sefer Torah 10,6 that holding a Torah is a mitzvah)
Is there any discussion on this matter in the halachik literature?