Modeling powerful interactions is a critical challenge in Click-through rate (CTR) prediction, which is one of the most typical machine learning tasks in personalized advertising and recommender systems. Although developing hand-crafted interactions is effective for a small number of datasets, it generally requires laborious and tedious architecture engineering for extensive scenarios. In recent years, several neural architecture search (NAS) methods have been proposed for designing interactions automatically. However, existing methods only explore limited types and connections of operators for interaction generation, leading to low generalization ability. To address these problems, we propose a more general automated method for building powerful interactions named AutoPI. The main contributions of this paper are as follows: AutoPI adopts a more general search space in which the computational graph is generalized from existing network connections, and the interactive operators in the edges of the graph are extracted from representative hand-crafted works. It allows searching for various powerful feature interactions to produce higher AUC and lower Logloss in a wide variety of applications. Besides, AutoPI utilizes a gradient-based search strategy for exploration with a significantly low computational cost. Experimentally, we evaluate AutoPI on a diverse suite of benchmark datasets, demonstrating the generalizability and efficiency of AutoPI over hand-crafted architectures and state-of-the-art NAS algorithms.