Consider our scheme for natural language $(E,S,O, s, r)$ where $s: E\rightarrow S$ and $r : S \rightarrow O$ are the sense and reference functions (relations).
What is a word ? It is in general a complex $(e,s,o, S, R)$, consisting of an expression $e$, its meaning $\sigma$, its reference $o$ and the relationships themselves $S$, $R$, existing between $e$ and $s$ and $s$ and $o$ respectively.
Every element or subsystem of the complex can itself be an object, an element of $O$. For example I can talk about the relation between the expression 'rose' and the concept/meaning rose. We need syntactical devises to make this clear and unambiguous. When we throw around words like rose carelessly we are in general mixing many different entities and relations into one bag.
As Frege noted, the elements of $S$ can themselves be objects. Let $\sigma\in S$. Then there is a $w \in E$ and $\sigma' \in S$ such that $s(w) = \sigma'$ and $r(\sigma') = \sigma$. Why not have a sense which is its own reference ? Or a sense which has as reference the expression of which it is the sense of ? Or an expression whose reference is the expression itself ?
And what about aggregates of senses ? Indeed the reference of concepts are, perhaps, objects which are aggregates : the extension of rose. We need a syntactic devise for this too...
In CIL models we need to introduce a subset $E \subset D_{-1}$ which consists of a model-theoretical representation of the expressions of the language. We could then internalize $s$ by a predicate $\Delta_E (e, p)$ which reads: the (closed) expression $e$ has sense $p$. But how do we treat $s$ itself as an object ? If we consider that every subset of $D$ has a representative in $E$ then it seems this will lead to trouble...
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