Museums aim at offering personalized visits to encourage visitors to visit more than once. Few approaches consider the specific skills of museum professionals when designing tools for this purpose. We conducted a three-step iterative and user-centered design process with 13 museum professionals from six museums. This analysis led us to a main finding: the most complicated task for museum professionals is to explore their design space, composed of all possible visitor profiles for which to create visits. We propose a visualization for this multidimensional design space and six potential interactions on this representation. In an exploration space, we classify them on two axes: the selection approach and the type of interface (GUI versus TUI). We analyze their benefits and limits and, based on a pilot study, we propose insights and questions for future design.