Mainstream core grammar theory, still to some extent relying on the idealized speaker in a homogeneous speech community, is ill equipped to handle different kinds of periphery data, like code-switching data and other types of language mixing data. In this paper, we defend a model of grammar that we argue is able to handle different types of both core and periphery data. Empirically, we focus on single-word code-switching data obtained from a small corpus of the Chinese production of a bilingual Mandarin Chinese -Norwegian child. We develop the beginnings of a generative frame model of grammar exploiting insights both from late insertion neo-constructional models and from code-switching theories assuming a matrix -embedded language asymmetry. We will be paying special attention to the lexicon -syntax interface.