Integrated Modular Avionics (IMA) enables incremental qualification by encapsulating avionics applications into software partitions (SWPs), as defined by the ARINC 653 standard. SWPs, when running on top of single-core processors, provide robust time partitioning as a means to isolate SWPs timing behavior from each other. However, when moving towards parallel execution in many-core processors, the simultaneous accesses to shared hardware and software resources influence the timing behavior of SWPs, defying the purpose of time partitioning to provide isolation among applications. In this paper, we extend the concept of SWP by introducing parallel software partitions (pSWP) specification that describes the behavior of SWPs required when running in a many-core to enable incremental qualification. pSWP are supported by a new hardware feature called guaranteed resource partition (GRP) that defines an execution environment in which SWPs run and that controls interferences in the accesses to shared hardware resources among SWPs such that time composability can be guaranteed.