Cool... it sounds like maybe you aren't unhappy with your speakers, but with bass... and just want to add more speakers as well?
And that vaulted ceiling might actually be more helpful than you realize, from an acoustics perspective!
Any way... For subs, measure your open area room for
total volume. For that cathedral ceiling, figure for the lower part of the whole room up to the 8'height... then figure the volume for the sloped ceiling by treating the height as 4'(the highest point of the slope) x same L xW as below, and simply divide by 2 (volume of the ceiling portion), and add that to the volume of the room below.
This room volume is where you will start to figure how much woofage you might need.
I know I need to either upgrade the receiver or get a separate amp to add channels that way.
The separate amp won't add channels without the AVR being able to process.
So, that leaves your budget!
Once you shop around a little, looking at AVRs that can amplify 9 channels and process 11, Decide on what you want to spend on it. If you go with the older models like Marantz SR6012, a comparable Denon... they are pretty heavily discounted right now... just a hint. Best I can tell, the newer models of those two lines are just updating to IMax compatibility with a few other minor tricks here and there... not high on my value list. But only you can decide what you want for yourself.
After you figure out your AVR, look at subs. I would recommend looking for something that will work in your room size, first, that drops down to ~18Hz, and can perhaps even be daisy chained with another sub. You will want to buy the same matching subs as you go forward (this will help you avoid some problems with bass response). My recommendation is to replace the Klipsch with the best single sub you can allow yourself to afford now, then start saving for the second, and perhaps third. (Thanks William for teaching me that!)
Lastly, consider that you can hang speakers from the ceiling without cutting into the ceiling. There is hardware for cathedral ceilings... just another option for you. Either way, I would do this after the AVR and Sub.
My 2 cents.
Keep sharing Alfred, we'll gladly help you make sense of everything!