Politics, like economy, is always a matter of supplies meeting demands. Is this likely to occur also for the sovereigntist claims formulated by populist parties? This paper investigates the political construction of sovereigntist discourse by populist parties and how it is likely to meet the demands of a country’s voters. By using data from elite and public opinion surveys, as well as of expert surveys, this article will assess the multidimensionality of the concept of sovereignism and whether this applies to the different actors involved, namely parties, elites, and voters. In particular, we classify sovereignism, by considering the three main claims that originate from the spheres of sovereignty that are challenged by contemporary transformations, and namely: Economic Cultural, and Political sovereignism. Populism then re-elaborates on these three dimensions, by providing ideological constructions of the people against the elite. In this article we expect to shed light on at least two aspects: first, that there is no single sovereignism, not only in the supply side, but also in the demand side; second, whether and to what extent populist parties are likely to capitalise on the different dimensions of sovereignism, and mobilise voters on all of them.