Ideological scaling is an ubiquitous tool for inferring political opinions of users in social networks, allowing to position a large number of users in left-right or liberal-conservative scales. More recent methods address the need, highlighted by social science research, to infer positions in additional social dimensions. These dimensions allow for the analysis of emerging divisions such as anti-elite sentiment, or attitudes towards globalization, among others. These methods propose to embed social networks in multi-dimensional attitudinal spaces, where dimensions stand as indicators of positive or negative attitudes towards several and separate issues of public debate. So far, these methods have been validated in the context of individual national settings. In this article we propose a method to embed a large number of social media users in multi-dimensional attitudinal spaces that are common to several countries, allowing for large-scale comparative studies. Additionally, we propose novel statistical benchmark validations that show the accuracy of the estimated positions. We illustrate our method on Twitter friendship networks in France, Germany, Italy, and Spain.