The codegree Turán density $γ(F)$ of a $k$-graph $F$ is the smallest $γ\in[0,1)$ such that every $k$-graph $H$ with $δ_{k-1}(H)\geq(γ+o(1))\vert V(H)\vert$ contains a copy of $F$. We prove that for all $k,r\in\mathbb{N}$ with $k\geq3$, $\frac{r-1}{r}$ is an accumulation point of $Γ^{(k)}=\{γ(F):F\text{ is a }k\text{-graph}\}$. This makes progress on a problem posed by Mubayi and Zhao.