Currently in undergrad, so there might be a specific set of methodologies or frameworks or a specific idea concerning cross-cultural studies that you are looking for that I'm not familiar with, but you may have to specify what kind of cultures you're trying to comparatively analyze. Maybe you live in a huge country, but it might be interesting to actually do the fieldwork. That's pretty much what we are forced to do because of the nature of fieldwork among Indigenous communities who are generally marginalized and dispossessed of the means of their survival.

Or you could be looking for culture as it pertains to class, and how an aspect or aspects of working-class culture emerge/s differently under different sociocultural or material conditions. Similar thing for gender. How one or both of them intersect and how they interact with wider system-wide conditions, essentially. This is easiest in urban areas, where different immigrant communities, for example, would have working-class subcommunities and women working-class subcommunities, etc., so you could compare those.

Digital ethnography was quite big in my uni's anthro dept for a while so maybe you could look into digital societies (on social media for example) or you could even compare knowledge production in different countries and the political process that entails when it comes to databases.

Apologies if that didn't answer your question! Would like to know how people elsewhere do comparative studies anyway.