Sure you can have as many drill down categories as you want and, in Theater and Remote mode views you can also tick the option to show all which you should experiment with. You can also duplicate the same field (ex. Albums then Expression (Albums only with 4-5 stars or Artists); Artists Grouped alphabetically, A-C, D-F etc, drill down to Artists again, but it would filter just the A-C artists etc.) There are a bunch of ways. Depending on how you want it to show up on the screen.
What you probably want is Album Artist (or Artist depending on how you want to show compilations)=>Album=>an expression to include the Rating field only showing 4-5 stars (set grouping to 1) with the show all option set. You could also have album artist=>Album=>Album (expression based on only 4 or 5 stars). You have Album Artist=>Album=>Rating as another possibility. Not sure -- why don't you experiment?
The name variable only works for Standard Mode views, if that is what you are referring to. Each tier category (or drill down) you have a bunch of choices when you hit add (field, path, expression etc.)
I'd post expressions for you but don't have the time now. More importantly, you wouldn't learn anything that way.
BTW other than the show all option available (only in Remote and Theater mode views), and the thumbnail text display (only in Standard mode category views), I suggest playing around with a new category view in Standard mode first, at least for testing. That way you can then import it directly into the Remote or Theater mode sections -- finally just tweak it if needed (like the show all option, the order, nesting etc.)