A Haptic Experience may take many shapes or forms, ranging from simple UI notifications on a phone, to fully immersive multi-sensorial experiences. In this context, dedicated Haptic authoring tools have been flourishing and the literature on Haptic design introduced many concepts and guidelines to improve Haptic Experiences. In this paper, we propose to go beyond haptic design and explore the potential of end-user customization of Haptic Experiences. First, we discuss and extend a theoretical model of Haptic Experience. We revisit the proposed design parameters to account for the spatialized notion of haptic feedback and study the suitability of these parameters for end-user customization. Then, we detail a user study (n = 52) exploring how users can customize different haptic effects (18 different effects) through haptic customization parameters, i.e., intensity and spatial density. Finally, our results indicate significant variability in these parameters depending on the context and provide directions for future user studies regarding haptic profile design determined by subjective data.