  The metrical theory of the product of consecutive partial quotients is
associated with the uniform Diophantine approximation, specifically to the
improvements to Dirichlet's theorem. Achieving some variant forms of metrical
theory in continued fractions, we study the distribution of the at least two
large partial quotients with product forms among the first $n$ terms. More
precisely, let $[a_1(x),a_2(x),\ldots]$ be the continued fraction expansion of
an irrational number $x\in(0,1),$ and let $\varphi\colon \N\to\R$ be a
non-decreasing function, we completely determine the size of the set
\begin{align*} \mathcal{F}_2(\varphi)=\Big\{x\in[0,1)\colon \exists ~1\le k\neq
l \le n, ~&a_{k}(x)a_{k+1}(x)\ge \varphi(n), \\&a_{l}(x)a_{l+1}(x)\ge
\varphi(n) \text{ for infinitely many } n\in \N \Big\} \end{align*} in terms of
Lebesgue measure and Hausdorff dimension.
