We prove a Steinhaus-type theorem for four-dimensional matrix transformations of double sequences, establishing that $(\mathcal L_1,\mathcal L_1,P)\cap(\mathcal L_s,\mathcal L_1)=\emptyset$, $s>1$. This extends Fridy's classical result for single sequences. Our results hold for sequences of bounded variation, bounded, Pringsheim convergent, bounded Pringsheim convergent, and regularly convergent sequence spaces. We show this theorem fails in non-archimedean fields through a counterexample.