If contact-induced grammaticalization, as Heine and Kuteva propose, resembles unidirectional, monolingual grammaticalization, how then do we handle instances of rearrangement of the semantic meaning and scope of case markers? This problem is discussed by comparing and contrasting a sample of so-called Northeastern Romani dialects (see Matras, 2002), with their respective contact languages (Russian and Polish). Using semantic maps, it is shown how the Romani dialects in question restructure their case representation system to adjust to the systems of the model languages, and it is debated what exactly gets assimilated when two languages come into contact.