A group of permutations $\Gamma$ of a set $E$ is called r-ply transitive if, for any two sequences $(a_1,a_2,\ldots,a_r),(b_1,\ldots,b_r)$ of $r$ distinct elements of $E$, there exists a permutation $\sigma\in\Gamma$ such that $\sigma(a_i)=b_i$ for $1\leq i\leq r$, this property not holding for at least one ordered pair of sequences of $r+1$ distinct elements of $E$.
Is the bolded part necessary? I have never seen a definition of multiple transitivity that includes it. Why add it?