I have three variables: $y$, $x_1$ and $z$.
I'm interested in finding the effect of $x_1$ on $y$. Unfortunately $x_1$ is endogenous so I use an instrument z.
I know that $z$ is correlated with $x_1$. The problem is, $z$ is correlated with another variable ($x_2$) that arguably has an effect on $y$. $z$ is unlikely to have a causal effect on $x_2$, but $x_2$ may still be endogenous for other reasons (e.g. reverse causality, etc.).
Will the following procedure give me a consistent estimate of beta-1: two stage least squares with $y$ regressed on $x_1$ and $x_2$, with $z$ as an instrument for $x_1$?