This paper presents a method for constructing integrable couplings using two-dimensional unital algebras. It demonstrates that such algebras can generate two types of integrable couplings: perturbation-type and nonlinear-type. The approach involves linear expansions of variables and operators within the algebraic framework, leading to the derivation of integrable couplings for equations like the KdV equation and the AKNS system of nonlinear Schrödinger equations. The paper provides explicit forms of Lax pairs and hereditary recursion operators for these couplings. It also explores the use of $ M_2 $-extensions, which involve additional algebraic structures, to generate more complex integrable systems. The study highlights the importance of two-dimensional unital algebras in the classification and construction of integrable equations, offering new insights into their algebraic and structural properties. The results contribute to the broader understanding of integrable systems and their applications in mathematical physics.This paper presents a method for constructing integrable couplings using two-dimensional unital algebras. It demonstrates that such algebras can generate two types of integrable couplings: perturbation-type and nonlinear-type. The approach involves linear expansions of variables and operators within the algebraic framework, leading to the derivation of integrable couplings for equations like the KdV equation and the AKNS system of nonlinear Schrödinger equations. The paper provides explicit forms of Lax pairs and hereditary recursion operators for these couplings. It also explores the use of $ M_2 $-extensions, which involve additional algebraic structures, to generate more complex integrable systems. The study highlights the importance of two-dimensional unital algebras in the classification and construction of integrable equations, offering new insights into their algebraic and structural properties. The results contribute to the broader understanding of integrable systems and their applications in mathematical physics.