Hyperreconfigurable architectures can adapt their reconfiguration abilities during run time and have been proposed to increase the speed of dynamic reconfiguration. They use two types of dynamic reconfiguration steps. In hyperreconfiguration steps they change their ability for reconfiguration and in ordinary reconfiguration steps they reconfigure the actual contexts for a computation within the limits that have been set by the last hyperreconfiguration step. In this paper we study the concept of partial hyperreconfiguration for multi tasks environments. We propose several models for partially hyperreconfigurable architectures and study corresponding reconfiguration problems to find optimal (hyper)reconfigurations. While under a general cost model the problem to find optimal (hyper)reconfigurations is known to be NP-complete even for a single task. We identify an interesting special case that can be solved by a polynomial time algorithm even for multiple tasks. We illustrate the introduced concepts with a partially hyperreconfigurable example architecture and describe the results of simulated runs with a small test application.