<p>This paper investigates the application of the Kadomtsev–Petviashvili reduction method to generate rogue wave solutions for nonlinear evolution equations. While this method provides a systematic algebraic approach through determinant representations and tau-functions, its applicability to extended nonlinear models has not yet been thoroughly explored. In this work, we successfully apply this framework to a completely integrable extended Kadomtsev–Petviashvili equation, which serves as a significant model for nonlinear wave dynamics across multiple physical contexts. The key novelty of our study lies in deriving a bilinear representation of the equation within the Kadomtsev–Petviashvili hierarchy reduction method and in obtaining new families of rational solutions expressed algebraically through Schur polynomials. These solutions produce higher-order rogue waves and rational soliton lines, whose dynamics are analyzed in detail. By appropriately selecting the free parameters, we demonstrate that the tau-functions reduce to even-power polynomials, thereby unifying and generalizing previously reported solutions obtained using symbolic computation. The proposed reduction framework not only clarifies the algebraic structure of rogue waves for the model under consideration but also demonstrates its versatility for application to other extended or reduced forms of this model.</p>