The present study examines both properties of the language and properties of the learner to better understand variability at the earliest stages of second language (L2) acquisition. We used event-related potentials, an oral production task, and a battery of individual differences measures to examine the processing of number and gender agreement in two groups of low-proficiency English-speaking learners of Spanish who were tested in multiple sessions. The results showed an advantage for number, the feature also instantiated in the native language, as both groups showed a native-like P600 response to subject-verb and noun-adjective number violations across sessions. The more advanced group showed larger effects for number and marginal sensitivity to gender violations. These results suggest that native-like processing of shared features is possible even for novice learners, contrary to proposals suggesting that all morphosyntactic dependencies are initially processed in a non-native manner. Working memory (WM) was a predictor of P600 effects for number and also for gender (where the effect was marginal), suggesting that similar abilities may capture variability in the processing of both shared and unique features despite differences in overall sensitivity. Furthermore, whereas WM predicted performance on online tasks (P600 effects/oral production), verbal aptitude predicted performance on tasks examining morphosyntactic accuracy (grammaticality judgment task/oral production). Our results show that the linguistic properties of the L2, the individual characteristics of the learner, and the nature of the task at hand all play an important role in capturing the variability often observed in the L2 processing of agreement.