Software engineers are acutely aware that the build of software is an essential but resource-intensive step in any software development process. This is especially true when building large systems or highly configurable systems whose vast number of configuration options results in a space explosion in the number of versions that should ideally be built and evaluated. Linux is precisely one such large and highly configurable system with thousands of options that can be combined. Previous study showed the benefit of incremental build, however, only on small-sized configurable software systems, unlike Linux. Although incremental compilation for post-commit is used in Linux, we show in this paper that the build of large numbers of random Linux configurations does not benefit from incremental build. Thus, we introduce and detail PyroBuildS, our new approach to efficiently explore, with incremental builds, the very large configuration space of Linux. Very much like fireworks, PyroBuildS starts from several base configurations ("rockets") and generates mutated configurations ("sparks") derived from each of the base ones. This enables exploring the configuration space with an efficient incremental build of the mutants, while keeping a good amount of diversity. We show on a total of 2520 builds that our PyroBuildS approach does trigger synergies with the caching capabilities of Make, hence significantly decreasing builds time with gains up to 85%, while having a diversity of 33% of options and 15 out of 17 subsystems. Overall, individual contributors and continuous integration services can leverage PyroBuildS to efficiently augment their configuration builds, or reduce the cost of building numerous configurations.