Discrimination refers to an unjust or prejudicial difference in the treatment of an individual based on the membership, or perceived membership, to a certain group or category. These categories, sources or ‘grounds’ include gender, race, sexual orientation, and so on. Acknowledging that discrimination may be directed against these many different subgroups within a population requires to also acknowledge that individuals may be exposed to potential discrimination based on several grounds; they may face `multiple discrimination'. While in the literature, the grounds for discrimination are typically considered separately, in certain circumstances, in order to appropriately describe the discriminatory treatment that a person experiences, the grounds must be considered together. After theoretically outlining the different ways in which an individual may be discriminated against based on several grounds -- we define sequential, simple, compound, intersectional and regressive discrimination -- we investigate the following three research questions: How do people discriminate when identities are multi-dimensional? Is there `intersectional' or `compound'' discrimination? How important is it? We do so by running a pre-registered laboratory experiment with 279 participants over treatment- and control condition. To model discrimination, we rely on social identity theory and define discrimination as the difference between in-group and out-group bias. In this setting in which we only investigate artificial identities and there is only taste-based discrimination, we find little intersectional/compound discrimination.