The European 2020 Strategy has launched a novel indicator for monitoring poverty reduction over the current decade, simultaneously taking into account income, material deprivation and work intensity. The present paper uses this new indicator as a springboard for a discussion of the potential of a multidimensional measure, based on these three domains, to analyse the risk of poverty and social exclusion among immigrants. It is argued that the analytical insight and internal consistency of the new Europe 2020 indicator can be enhanced by a more structured measurement approach, relying on some recent advances generated by multidimensional poverty literature. The Alkire-Foster methodology provides a natural extension to the Europe 2020 indicator, which can usefully complement the picture drawn from the at-risk-of-poverty or social exclusion statistics. In the second part of the paper, these adjusted measures are used to analyse the multidimensional poverty profiles of immigrant households in Spain and other five developed countries, as well as the changes occurring since the beginning of the economic downturn. We try to show that the Europe 2020 indicator alone may not be sufficient to reflect the growing intensity of multidimensional deprivation among immigrants in some countries.