You should be fine by entering multiple genre tags in the mp3 metadata genre field – just make sure you use a separator that works with the app you use to edit the metadata (e.g. commas or slashes – this might vary based on the app you use)
The standard for separating multiple entries in MP3 tags is the forward slash ‘/’. Plex will honor that (Plex also honors semicolons), but Plex only takes the first two genres that it finds in the tag. There’s a feature request to change that.
EDIT: Actually, Plex seems to take more than two tags, but it only shows two when viewing the album details page.