Many people speak more than two languages. How do languages acquired earlier affect the learnability of additional languages? We show that linguistic distances between speakers' first (L1) and second (L2) languages and their third (L3) language play a role. Larger distances from the L1 to the L3 and from the L2 to the L3 correlate with lower degrees of L3 learnability. The evidence comes from L3 Dutch speaking proficiency test scores obtained by candidates who speak a diverse set of L1s and L2s. Lexical and morphological distances between the L1s of the learners and Dutch explained 47.7% of the variation in proficiency scores. Lexical and morphological distances between the L2s of the learners and Dutch explained 32.4% of the variation in proficiency scores in multilingual learners. Cross-linguistic differences require language learners to bridge varying linguistic gaps between their L1 and L2 competences and the target language.