Let $R$ be a ring. Recall that a module $M$ is called finitely presented if there is an exact sequence

$R^n \to R^m \to M \to 0$.

with $n,m \in \mathbb{N}$. A well known result states that any module $M$ is a filtered direct limit of finitely presented modules. A bit more generally, we can call a module $M$ 2-finitely presented if there is an exact sequence

$R^k \to R^n \to R^m \to M \to 0$

with $k,m,n \in \mathbb{N}$.

My question is: is any module the filtered direct limit of 2-finitely presented modules? what about higher order presentation?