I have found over the years, that actors never really know how they do in their auditions. When you think you've knocked it out of the ballpark, you get feedback that you were too theatrical. When you think you were horrible and don't care, you book the part. So, asking to do your audition over again, could be the worst thing you can do. Maybe you should quit while you are ahead.
Don't ask if you can do it again a different way. 75% of the time, in my experience, we let you do it again to see what different way you are going to come up with. And you do it again the exact same way. The comment from Producers and Directors is usually, "I really liked what that actor did the first time, and then when they asked to do it a second time a different way, all they showed me was they are not versatile."
Don't ask the Casting Director, Director or Producer "Do you want to give me some direction?" Depending on the "tone" you say this in, it can be misconstrued that they are not doing their job or as you being too pushy. The best way to exit the room after you finish the audition is to look them in the eye and say "Anything else?". This puts the ball in their court to adjust you or get you out the door!