This study investigates how postlexical phonological processes are acquired in multilingual speech, namely, how learners cope with conflicting demands in the production and perception of the voicing patterns in their non-native languages, what impact lexical knowledge has on learner behavior, and to what extent existing speech learning models can account for it. To investigate this, 14 Hungarian native speakers, proficient sequential learners of Spanish and English, took part in two types of experiment. The production experiments examined regressive voicing assimilation between obstruents and when the trigger was a sonorant consonant (presonorant voicing) word-internally and across word-boundary. At word level, we compared various lexical groups: non-cognates, double cognates and triple cognates (inhibitory, facilitative, and cognates with conflicting information). The perception experiments aimed to find out whether learners notice the voicing assimilations mentioned. The results showed that participants failed to learn presonorant voicing and failed to block regressive voicing assimilation despite perceiving the latter as linguistically relevant. Data also revealed that there is no direct link between perception and production, and that cognate status had a limited effect, but in triple cognates the primacy of the native language was dominant. Thus, it is concluded that in laryngeal postlexical processes the native language plays the primary role, neither the other non-native language, nor linguistic proximity seems to be decisive. Our data can be best accounted for by the Scalpel Model extended to phonological acquisition.