The Segment Anything model (SAM) has shown a generalized ability to group image pixels into patches, but applying it to semantic-aware segmentation still faces major challenges. This paper presents SAM-CP, a simple approach that establishes two types of composable prompts beyond SAM and composes them for versatile segmentation. Specifically, given a set of classes (in texts) and a set of SAM patches, the Type-I prompt judges whether a SAM patch aligns with a text label, and the Type-II prompt judges whether two SAM patches with the same text label also belong to the same instance. To decrease the complexity in dealing with a large number of semantic classes and patches, we establish a unified framework that calculates the affinity between (semantic and instance) queries and SAM patches, and then merges patches with high affinity to the query. Experiments show that SAM-CP achieves semantic, instance, and panoptic segmentation in both open and closed domains. In particular, it achieves state-of-the-art performance in open-vocabulary segmentation. Our research offers a novel and generalized methodology for equipping vision foundation models like SAM with multi-grained semantic perception abilities. Codes are released on https://github.com/ucas-vg/SAM-CP.