Multilingual text compression exploits the existence of the same text in several languages to compress the second and subsequent copies by reference to the first. This is done based on bilingual text alignment, a mapping of words and phrases in one text to their semantic equivalents in the translation. A new multilingual text compression scheme is suggested, which improves over an immediate generalization of bilingual algorithms. The idea is to store the necessary markup data within the source language text; the incurred compression loss due to this overhead is smaller than the savings in the compressed target language texts, for a large enough number of the latter. Experimental results are presented for a parallel corpus in six languages extracted from the EUR-Lex website of the European Union. These results show the superiority of the new algorithm as a function of the number languages.