The flesh to stone spell states:
A creature restrained by this spell must make another Constitution saving throw at the end of each of its turns. If it successfully saves against this spell three times, the spell ends. If it fails its saves three times, it is turned to stone and subjected to the petrified condition for the duration. The successes and failures don’t need to be consecutive; keep track of both until the target collects three of a kind.
Say a wizard casts flesh to stone on an enemy, an orc to make it simple, and the orc fails the first saving throw.
Then the wizards friend, in the same round, casts a second flesh to stone spell on the poor orc, to which he also fails his saving throw. Then the wizards other friend casts a third flesh to stone in that same round on the poor orc and he fails that saving throw as well.
Does the orc fully petrify in that round? In other words, do the effects of the spells starting to petrify the orc stack with each other? He did fail 3 saving throws but it was against 3 separate spells instead of one spell.