A number of hardware systems have been built or proposed to provide an interface for software to influence cache management. The combined software-hardware solution is called collaborative caching. Our previous work showed that in theory collaborative caching with LRU and MRU may enable a program to manage cache optimally. In this work we first present a prioritized LRU model. For each memory access, a program specifies a priority, the target cache position for the accessed datum, for all cache sizes. We have proved that the prioritized LRU holds inclusion property. Alternatively, we describe a dynamic cache control scheme based on the associated priority. The limitation of knowing cache size in our LRU-MRU collaborative caching work is removed.