We present a new GPU-based rendering system for ray casting of multiple volumes. Our approach supports a large number of volumes, complex translucent and concave polyhedral objects as well as CSG intersections of volumes and geometry in any combination. The system (including the rasterization stage) is implemented entirely in CUDA, which allows full control of the memory hierarchy, in particular access to high bandwidth and low latency shared memory. High depth complexity, which is problematic for conventional approaches based on depth peeling, can be handled successfully. As far as we know, our approach is the first framework for multivolume rendering which provides interactive frame rates when concurrently rendering more than 50 arbitrarily overlapping volumes on current graphics hardware.