Question about splitting data

I am wondering what the most common way to handle data is wherein a participant belongs to multiple groups. For example, if you're wanting to run linear regression and look at how specific diet-type (IV) effects a specific health outcome (DV/response variable) and you have participants that are on a combination of 2 diet types (lets say "Mediterranean" AND "Vegetarian") and you actually want to know how Mediterranean outcomes are different than Vegetarian, how do you handle those participants? I know you could make another group that's a combination diet type, but not if you have too small of an N. Any input is appreciated!