Not possible to build into cathedral ceiling?
Generally nothing's really impossible, but a lot of things are impractical, usually due to expense.  

Depending on the size of the room, changing a two story room into two stacked one-story rooms is a big job and will require an engineer's stamp, but nothing magic.  

Essentially all you're doing is inserting a floor at ceiling height.  You'll have to provide for a means of access to the new space - might be as simple as a set of stairs up, or cutting a door into an upstairs hallway.  

The extra load of the structure (and the contents and the occupants) will have to be taken into consideration.  For example it's possible that two opposite existing walls are strong enough to carry the additional load to the foundation, and the distance can be spanned by trusses.  

There will probably be many possible ways to do it and doing a careful comparison of costs could save you a bundle.  

There will be a million details to deal with - maybe redoing forced hot air ductwork, electrical, moving windows, etc. - etc.  

It may be that it's not impossible at all, but an addition gives you much more for your money.