Transfer of syntactic structures from the first language (L1) is a phenomenon that has been under study as long as second language acquisition (SLA) has been an established research field. Only recently, multilingual backgrounds of learners have been considered and transfer into a third language (L3), from either L1 or L2, or both, has developed into an area of particular interest. In this talk I will present some models proposed for transfer in L3 syntax and point at some studies that combine different background and target languages. The models – The Cumulative Enhancement Model, The L2 Status Factor Model, and The Typological Primacy Model – have several times been confronted and tested by researchers in the field of multilingualism/L3 learning. These models are based on different factors that seem to play important roles for the initial state of L3 learning (mainly typological and cognitive similarity between languages). Up to now, results have diverged, and it has not been possible to rule out any of these models. Instead, researchers continue to debate and argue in favour of one or the other model. A more fruitful way of going ahead now seems to be to try to formulate theories of how these and other factors interact and also of what happens beyond the initial state.