  We determine the structure of the set of intermediate $\beta$-shifts of
finite type. Specifically, we show that this set is dense in the parameter
space $\Delta = \{ (\beta, \alpha) \in \mathbb{R}^{2} \colon \beta \in (1, 2)
\; \text{and} \; 0 \leq \alpha \leq 2 - \beta\}$. This generalises the
classical result of Parry from 1960 for greedy and (normalised) lazy
$\beta$-shifts.
