As a result of being a head coach of the Georgian women's Olympic team, the team got the second place on The 34th Chess Olympiad in Istanbul. Since 2004, he was also working with the Georgian men's team. Concretely, he was working with Zurab Azmaiparashvili, Baadur Jobava, Giorgi Kacheishvili, Zviad Izoria, Mikheil Mchedlishvili, Levan Pantsulaia, Tamaz Gelashvili, Konstantine Shanava, David Jojua, Tornike Sanikidze, Giorgi Margvelashvili, David Arutinian, Merab Gagunashvili, Dawit Schengelia, Valeriane Gaprindashvili. As for the women's team, except Maia Chiburdanidze, Supatashvili trained grandmasters – Nino Khurtsidze, Salome Melia, Lela Javakhishvili, Maia Lomineishvili, Meri Arabidze, Sopiko Khukhashvili, Natalia Edzgveradze.