Can you add a second story above a vaulted ceiling?

My question to you is: are you planning to keep the vaulted ceiling? And if so, how do you envision the arrangement of the 2nd story above the 1st? How are you going to utilize the space above the sloped sides of the existing ceiling and below the floor of the new 2nd story?

You can do anything with enough time and money. One key issue when adding a second story above an existing room is whether the existing ceiling joists are properly sized to serve as floor joists for a living space. Typically they are not, so adding a second floor often requires replacing the existing ceiling joists.

As Ebaines noted "You can do anything with enough time and money". I use this saying when people ask me if …… can be done. Your question leaves a lot to ask. How high is the vaulted ceiling, what is the slope angle, what is above the vault, construction features, bearing walls, access to new space etc. You need to install bearing walls, new floor joists/trusses, stairways, most likely landings as code restricts a 12 ft. rise before a landing is needed, emergency egress (people usually forget that), windows to code, add wiring, HVAC and other things I have omitted. If you are serious about doing something like this, first contact the local permitting agency to see if they would allow and then start getting ideas and quotes from insured, licensed building contractors. This is definitely not a DIY project. ,

You could add a second story but you will lose the vaulted ceiling. Consider expanding out instead of up. It is usually more cost efficient if you have the space.