This paper proposes an efficient algorithm for edge-preserving filtering with multiple guidance images, so-called multilateral filtering. Multimodal signal processing for sensor fusion is increasingly important in image sensing. Edge-preserving filtering is available for various sensor fusion applications, such as estimating scene properties and refining inverse-rendered images. The main application is joint edge-preserving filtering, which can preferably reflect the edge information of a guidance image from an additional sensor. The drawback of edge-preserving filtering lies in its long computational time; thus, many acceleration methods have been proposed. However, most accelerated filtering cannot handle multiple guidance information well, although the multiple guidance information provides us with various benefits. Therefore, we extend the efficient edge-preserving filters so that they can use additional multiple guidance images. Our algorithm, named decomposes multilateral filtering (DMF), can extend the efficient filtering methods to the multilateral filtering method, which decomposes the filter into a set of constant-time filtering. Experimental results show that our algorithm performs efficiently and is sufficient for various applications.