In enriched category theory over a base monoidal category $(\mathcal{V},\otimes_{\mathcal{V}},\mathbf{1}_{\mathcal{V}})$, one can consider $\mathcal{V}$ itself as a $\mathcal{V}$-enriched category when it has a closed monoidal structure $[-,-]_{\mathcal{V}}$.

Is there a similar procedure in internal category theory? That is, starting from a category $(\mathcal{E},\times_{\mathcal{E}},\mathbf{1}_{\mathcal{E}})$ with pullbacks and a terminal object, can one associate an $\mathcal{E}$-internal category to $\mathcal{E}$ itself?