Add a custom sort by value

[atomicheg]

I have a sushi-shop and there are several sushi categories: for ex. cat1 cat2 and cat3. Some of those shushi can be spicy or vegetarian, i need to put new options in sort by: spicy and vegetarian, so you can choose for ex. cat1 then click on sort by dropdown menu -> select vegetarian and you will be shown only those sushi which belong to cat1 and are vegetarian and the same logic should be for cat2 -> spicy, cat3 -> vegatarian and so on. How can i do this ? Any help would be appreciated.