Non-predictably evolving applications are applications that change their resource requirements during execution. These applications exist, for example, as a result of using adaptive numeric methods, such as adaptive mesh refinement and adaptive particle methods. Increasing interest is being shown to have such applications acquire resources on the fly. However, current HPC Resource Management Systems (RMSs) only allow a static allocation of resources, which cannot be changed after it started. Therefore, non-predictably evolving applications cannot make efficient use of HPC resources, being forced to make an allocation based on their maximum expected requirements. This paper presents CooRMv2, an RMS which supports efficient scheduling of non-predictably evolving applications. An application can make "pre-allocations" to specify its peak resource usage. The application can then dynamically allocate resources as long as the pre-allocation is not outgrown. Resources which are pre-allocated but not used, can be filled by other applications. Results show that the approach is feasible and leads to a more efficient resource usage.