Then, in the study screen of the deck, a number of sub-menus equal to the number of variables created would show up, allowing the user to quickly change the filter parameters
It would make sense with large filters. Eg you want to review all the image occlusion cards that have a particular tag, then all the cloze cards and finally all the basic cards with that tag. Then you want to move on to another tag and review the cards in the same order based on the note type
It came to my mind as was trying to review cloze cards with about 7 clozes per note. I had 10 or so notes and i wanted to review only the 2nd card generated by each note, after that i needed to move to the 3rd card etc
I see how that would be a different way to edit the search filter, but not how it would be an improvement in ease or functionality. It seems like you can do exactly what you want already by editing an existing Filtered deck. Or you could use sidebar or saved searches in the Browse window and Edit > Create Filtered Deck from there to create these decks on the fly.