Studies on sustainable diets show a need for replacement of animal-based foods by plant-based foods, which is also called “the protein transition.” To gain insight into the acceptability of such diet shifts, this study evaluated which current food sources people consume at varying amounts of meat consumption. The study population consisted of 4,313 participants aged 1–79 years of the Dutch National Food Consumption Survey 2012–2016, which assessed diet using two nonconsecutive 24-h dietary recalls. A two-part statistical model was used that accounts for both repeated measures and the correlation between probability and amount of consumption. Results are presented for quartiles of low to high meat consumption, by age and sex. Depending on age and sex, a higher consumption of fish (>100%), nuts and seeds (73–156%), cheese (34–111%), and sweets and snacks (28–81%) is observed in the lowest quartile of meat consumption compared to the highest. For fish, nuts, seeds, and cheese, this increase is mainly due to probability of consumption (>100%, 61–93%, and 16–64%, respectively). For sweets and snacks, the increase is mainly due to the amount of consumption (26–72%). Probability of potato consumption is 29–51% lower at low meat consumption. Vegetable consumption is lower mainly due to amount of consumption (6–29%). The results from the two-part model suggest that shifting away from a traditional Dutch high meat-vegetable-potatoes pattern is associated with higher probability of consuming fish, nuts and seeds, and cheese, but also increased amounts of sweets and snacks. This illustrates that analyzing the probability and amount part separately in relation to behavioral or physiological determinants extends our understanding of the diet according to meat consumption. These insights are important when developing realistic and acceptable food-based dietary guidelines for meat reduction.