its very tough. you would be better off just picking one or the other. unless you know your body very well and can adjust accordingly just stick to one or the other.
Having done it myself I can say, with certainty, that yes you can. Look into something like a TKD or carb cycling-based recomp. Basically, consume carbs based around your work out days and then focus on protein/fats at a below maintanence on your off days. You won't see as dramatic effects as totally focusing on either/or cutting or bulking specifically...but that's not what you asked.
it can be done just like everything else it all depends on you. it is always more effective for muscle growth to bulk. the level of success you will have doing the cut/bulk lean/bulk whatever you want to call it depends on how well your body does with minimal nutrients. i personally could not do it at this point. 80lbs ago i may have had some success but i doubt it would have lasted long. i need massive amounts of food to grow and holding onto size is a bitch