This study addresses whether there is anything special about learning a third language, as compared to learning a second language, that results solely from the order of acquisition. We use a computational model based on the mathematical framework of Linear Discriminative Learning to explore this question for the acquisition of a small trilingual vocabulary, with English as L1, German or Mandarin as L2, and Mandarin or Dutch as L3. Our simulations reveal that when qualitative differences emerge between the learning of a first, second, and third language, these differences emerge from distributional properties of the particular languages involved rather than the order of acquisition per se, or any difference in learning mechanism. One such property is the number of homophones in each language, since within-language homophones give rise to errors in production. Our simulations also show the importance of suprasegmental information in determining the kinds of production errors made.