Sometimes I see contravariant and covariant indices of tensors interspersed, like, for example, $T^{i}_{\;j}{}^{\,k}$, but, as far as I currently understand, only the position of covariant indices with respect to other covariant indices, and contravariant indices with respect to contravariant, affects the behaviour of the tensor.
Is there any common purpose/benefit/meaning in interspersing indices of tensors? Should I interpret the tensor $T^{i}_{\;j}{}^{\,k}$ any differently than I would without the interspersed indices, $T^{ik}_{\;\;j}$?