What happens when atoms or ions are exposed to the highest laser intensities available? One interesting process is ionization to charge states way in excess of what has been deemed possible based on cross sections considered so far. Multiphoton ionization has been shown capable of producing ions such as Xe21+ with a single laser shot. This is possible only due to highly non-linear processes which need further study. I will present a Penning trap experiment designed for high-intensity laser experiments with ions under well-defined conditions. By use of trap-specific techniques, it is possible to prepare clean ion targets with well-controlled size, shape, density, position and mass-to-charge ratio for subsequent laser irradiation. Reaction products can be analyzed non-destructively and are hence available for further studies. We are currently setting up such an experiment here at GSI with a design aimed at high movability such that it may be client at various laser facilities. I will discuss the possibilities of such a use of a Penning trap setup at high-intensity lasers like for example FLASH, PHELIX, JETI or POLARIS.