Don... yes you can! All you have to do is to change keys at the appropriate places. Billy Joel starts in the key of C. Then at "Son can you play me, etc", he jumps up an octave. That's the hard part, right? Well, the song needs a lift right there, but the same effect can be had by changing keys. What seems to work here is going into the key of F. Then at "Now John at the bar", go back into the origional key of C.

Whenever changing keys in the middle of a song, it's important to preceed the new key with some sort of chord modulation, which can be creative, or as simple as injecting the dominant 7th of the new key (in this example, C7).

When listening to commercial arrangements you'll hear this sort of thing done all the time... and sometimes in such a creative way that it's a strong asset to the overall arrangement. However, when it's applied to a song that we've heard 100s of times, it'll seem "not right". Never-the-less, as musicians, we have a creative license to do this sort of thing... and after a few plays, it'll seem very acceptable. Give it a try on "Piano Man"... great song, BTW. You might like it.