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The multiclass classification problem has been applied to build a decision function to separate a set of data points into multiple classes. To solve this problem, a number of methods have been developed by extending binary classifications to multiclass classification. However, researches on how to effectively combine multiple hyperplanes to make a decision function are in its early stage. This paper proposes theoretic backgrounds which are useful for understanding the relationships among multiple hyperplanes from the analytic viewpoint. Based on key findings, an integrated framework that is able to effectively extend binary linear classifications to cover multiclass classifications is introduced. By doing so, a new comparison method which consists of multiple classes and essential hyperplanes is established. To construct all possible pairwise hyperplanes, state-of-the-art binary classification methods such as support vector machines(SVMs) and multi-criteria linear programming(MCLP) are used. Through experiments, the new multiclass classification model with essential hyperplanes shows superior performance than competing models. As a result, it is supported that the proposed multiclass classifier can address the overfitting problem by eliminating needless hyperplanes.