$\mathsf{NL}$ versus $\mathsf{NL}[2]$
You can show that $\mathsf{NL}[2] \subseteq \mathsf{NL}$ as follows. We are given an $\mathsf{NL}[2]$ machine $M$, and we want to simulate it with an $\mathsf{NL}$ machine $M'$. The first that $M$ does is to guess the state $\sigma$ of $M'$ after it finishes reading the witness tape for the first time. It then simulates two copies of $M$, one starting at $M$'s initial state, and the other starting at $\sigma$. After going through the witness tape, it verifies that the first copy has reached $\sigma$, and that the second copy has reached an accepting state.

In this way you can show that $\mathsf{NL}[O(1)] = \mathsf{NL}$.