Dzagnidze akatambira chikwata chenyika cheGeorgia muWomen's Chess Olympiad, Women's World Team Chess Championship uye Women's European Team Chess Championship. Chikwata chake chakahwina menduru yegoridhe kuDresden muna 2008; akahwina zvibodzwa 7/10. Muna 2014, paWomen's Chess Olympiad
MuTromsø, Norway, Dzanidze akahwina menduru yegoridhe yemunhu semutambi akanakisa pabhodhi rimwe, pamberi paHou Yifan. Mumakwikwi eWomen's World Team Championship, akahwina menduru yebronze yechikwata muna 2011 na2017. Mumakwikwi eEuropean Team Championship, Georgia yakahwina menduru yesirivheri muna 2005, 2009 na2017. Dzagnidze mumwe munhu bhodhi mana menduru yegoridhe muna 2007.