This study investigates the acquisition of there-constructions (with verbs other than be) in L2 English by native speakers of European Portuguese (EP) and French. Its main purpose is to test two opposing hypotheses on the end-state of L2 acquisition at the interfaces: the Interface Hypothesis (IH) and the L1+input Hypothesis (LIH). The former proposes that internal interfaces are, generally, unproblematic at the end-state of L2 acquisition, whereas external interfaces, like the syntax-discourse interface, are areas of permanent optionality due to processing inefficiencies associated with bilingualism. The latter, in contrast, advocates that structures at external interfaces generate problems at a near-native level iff their properties are different in the L1 and the L2 and they are infrequent in the input. By administering 2 untimed drag and drop tasks, 3 speeded acceptability judgement tasks and 1 syntactic priming task to a total of 80 participants, we tested the types of overt expletives, the types of intransitive verbs and the types of discourse contexts compatible with thereconstructions in advanced and near-native English. The results confirm the IH, but suggest that the LIH is not completely wrong.