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In this paper, we deal with register-driven variation from a probabilistic perspective, as proposed in Schäfer, Bildhauer, Pankratz, Müller (2022). We compare two approaches to analyse this variation within HPSG. On the one hand, we consider a multiple-grammar approach and combine it with the architecture proposed in the CoreGram project Müller (2015) - discussing its advantages and disadvantages. On the other hand, we take into account a single-grammar approach and argue that it appears to be superior due to its computational efficiency and cognitive plausibility.