First-order multi arity functions in dependent type?
I do not understand what you are asking for, as it seems that you are simply asking for record types. The comments are too terse for a normal discussion, so I will offer a solution here, and you tell us what is wrong with it. I will do it by way of an example.

Suppose we are given the following types:
\begin{align*}
&amp; \vdash A \ \mathsf{type} \\
x : A &amp; \vdash B(x) \ \mathsf{type} \\
x : A, y : B(x) &amp; \vdash C(x,y) \ \mathsf{type}
\end{align*}
We would like the type of "binary" dependent functions whose domain is something like $x : A, y : B(x)$ and the codomain is $C(x, y)$.

Let us write
$$
\{ \ell_1 : A_1, \ell_2 : A_2(\ell_1), \ldots, \ell_n : A_n(\ell_1, \ldots, \ell_{n-1})
\}
$$
for a dependent record type with fields $\ell_i$. Observe that this looks a lot like a chunk of a context. Given a term $p$ of the above type, write $p.\ell_i$ for the $i$-th projection.

Without any pattern matching the type of dependent functions from $x : A, y : B(x)$ to $C(x, y)$ can be written as
$$\Pi (p : \{x : A, y : B(x)\}) \,.\, C(p.x, p.y),$$
which is arguably not so nice. But since patterns for record types are irrefutable (they always match), we can also use pattern-matching to write
$$\Pi (\{x = x_0, y = y_0\}) \,.\, C(x_0, y_0).$$
or, if we dare use the same symbol for a field label and the bound variable (OCaml allows this, for instance),
$$\Pi (\{x, y\}) \,.\, C(x, y),$$
For such pattern matching to make sense we need to know ahead of time that the fields $x$ and $y$ have types $A$ and $B(x)$, respectively. In implementations of proof assistants this is typically not a problem as each record type has to be declared before it can be used. Otherwise, we can still write something like
$$\Pi (\{x : A , y : B(x)\}) \,.\, C(x, y)$$
to indicate the missing type information.

Of course, the same sort of ideas apply to $\lambda$-abstraction. Given
$$x : A, y : B(x) \vdash e(x,y) : C(x,y)$$
the term
$$\lambda \{x : A, y : B(x)\} \,.\, e(x,y)$$
will receive the above product type.

In any case, it seems that we can have pattern matching on the records and get precisely what you are asking for. I kindly ask that, in case this is not what you are asking for, you modify your question and provide some concrete examples of what you are looking for.