Models on L3/Ln acquisition differ with respect to how they envisage degree (holistic vs. selective transfer of the L1, L2 or both) and/or timing (initial stages vs. development) of how the influence of source languages unfolds. This study uses EEG/ERPs to examine these models, bringing together two types of bilinguals: heritage speakers (HSs) (Italian‐German, n = 15) compared to adult L2 learners (L1 German, L2 English, n = 28) learning L3/Ln Latin. Participants were trained on a selected Latin lexicon over two sessions and, afterward, on two grammatical properties: case (similar between German and Latin) and adjective–noun order (similar between Italian and Latin). Neurophysiological findings show an N200/N400 deflection for the HSs in case morphology and a P600 effect for the German L2 group in adjectival position. None of the current L3/Ln models predict the observed results, which questions the appropriateness of this methodology. Nevertheless, the results are illustrative of differences in how HSs and L2 learners approach the very initial stages of additional language learning, the implications of which are discussed.