The goal of this paper is twofold. First, I wish to discuss two sets of problematic cases that arose when I applied Myers-Scotton's (1993) Matrix Language Frame model of codeswitching to Arabic diglossic switching (Boussofara-Omar, 1999). The first set involves the co-occurrence of system morphemes from both varieties of Arabic within a single CP. The second set concerns CPs in which the word order is that of the dialect but the system morphemes are from Standard Arabic, and CPs in which clashes occur between the subcategorization restrictions of the two varieties of Arabic participating in diglossic switching. The Matrix Language Frame model neither predicts nor offers explanations for either case. Second, in an effort to provide an explanation to their occurrence, I revisit the same problematic sets in light of Myers-Scotton's sub-models: the 4-M model and the Abstract Level model (Myers-Scotton and Jake, 2000, 2001), the latest refined version of the MLF model.