# Illustrating a matrix assembly within the array environment

I'm having trouble aligning the parentheses of a matrix assembly (parentheses within the same matrix). Essentially, what I want to do is this (excuse the terrible paint-job):

Where the submatrix K1 and K2 overlap. K1 and K2, should be 6x6, and therefore the assembly is a 9x9 matrix. I'm primarily familiar with the array environment: is this a possibility there?

Some ideas: make 3 by 3 matrices, with large entries; in appropriate spots put smashed the matrices K1 and K2

\documentclass{article}
\usepackage{mathtools,delarray}

\newcommand{\lK}[1]{%
\text{\LARGE$K^{#1}$}%
}
\newcommand{\plK}{\phantom{\lK{1}}}

\begin{document}

$\begin{bmatrix} \mathrlap{\smash[b]{% \begin{array}[t]\lbrack{@{}ccc@{}}\rbrack \plK&\plK&\plK\\[3ex] \plK& \lK{1}& \plK\\[3ex] \plK&\plK&\plK \end{array} }} \plK&\plK&\plK&\plK&\plK\\[2ex] \plK&\plK&\plK&\plK&\plK\\[2ex] \plK&\plK&\plK&\plK&\plK \mathllap{\smash[b]{% \begin{array}[t]\lbrack{@{}ccc@{}}\rbrack \plK&\plK&\plK\\[3ex] \plK& \lK{2}& \plK\\[3ex] \plK&\plK&\plK \end{array} }}\\[2ex] \plK&\plK&\plK&\plK&\plK\\[2ex] \plK&\plK&\plK&\plK&\plK\\[2ex] \end{bmatrix}$
\end{document}