Two-level predictors deliver highly accurate conditional branch prediction, indirect branch target prediction and value prediction. Accurate prediction enables speculative execution of instructions, a technique that increases instruction level parallelism. Unfortunately, the accuracy of a two level predictor is limited by the cost of the predictor table that stores associations between history patterns and target predictions. Two-stage cascaded prediction, a recently proposed hybrid prediction architecture, uses pattern filtering to reduce the cost of this table while preserving prediction accuracy. In this study we generalize two-stage prediction to multi-stage prediction. We first determine the limit of accuracy on an indirect branch trace using a multi-stage predictor with an unlimited hardware budget. We then investigate practical cascaded predictors with limited tables and a small number of stages. Compared to two-level prediction, multi-stage cascaded prediction delivers superior prediction accuracy for any given total table entry budget we considered. In particular, a 512-entry three-stage cascaded predictor reaches 92% accuracy, reducing table size by a factor of four compared to a two-level predictor. At 1.5K entries, a three-stage predictor reaches 94% accuracy, the hit rate of a hypothetical two-level predictor with an unlimited, fully associative predictor table. These results indicate that highly accurate indirect branch target prediction is now well within the capability of current hardware technology.