We report on the collision-coalescence dynamics of drops in Leidenfrost state using liquids with different physicochemical properties. Drops of the same liquid deposited on a hot concave surface coalesce practically at contact, but when drops of different liquids collide, they can bounce several times before finally coalescing when the one that evaporates faster reaches a critical size, of the order of the capillary length. The bouncing dynamics is produced because the drops are not only in Leidenfrost state with the substrate, they also experience Leidenfrost effect between them at the moment of collision. This happens due to their different boiling temperatures, and therefore, the hotter drop works as a hot surface for the drop with lower boiling point, producing three contact zones of Leidenfrost state simultaneously. We called this scenario the triple Leidenfrost effect.