Short of expanding their space, there's a way to make said space hold twice as many CDs. The solution is as simple as swapping out the CD trays with ones that can hold 2 CDs.
Beneath the box in the image, there's a 4-drawer CD Chest with 384-CDs-in-single-cases capacity. It's larger then said box. My CD collection has clearly outgrown it. Until now.
Step 1: What you need.
You can buy these at SleeveCity.
I ordered a 100-Pack of 2-CD Smart Tray All Clear for $35.30 USD.
$28.00 + $7.30 for least expensive shipping option.
This covered about 1/3 of my collection. I'll get a 300-pack later and do the rest, and post the results.
Step 2: Do it one band/singer/category at a time.
In this example, I gathered together every Newsboys CD I had.
When you gather them together, ask yourself if you also have any in you car, or anyplace else.
Next is to put them in a particular order (see image 2).
I went by copyright date, which is usually the album release date, from earliest to latest.
I stood them up and shifted them left and right in pairs, save for one that doesn't have a mate yet, so I can pair them easier (see image 3).
Step 3: Take 2!
Remove CDs and set aside (image 2),
Remove the trays. I used my thumbnail, although a thin, flat, non-sharp, non-pointy tool will do.
Examples: Butter knife, plastic spoon, credit card, guitar pick.
Note: If you choose to use your thumb(or finger)nail, remember that it/they may get chewed up in the process.
Insert your thumbnail/tool in between the tray and the U-card (printed layer in between tray and case bottom), and pry the tray out. (see cross-section diagram, image 4) Avoid inserting your thumbnail/tool in between the the U-card and the case bottom because doing so might damage the U-card.
Then slide your thumbnail/tool along the edge of the tray until one corner pops out, then slide it the other way to pop the other corner, or just pull it out at this point (image 5).
Repeat for the other CD case. (image 6)
Add the trays to your Stack-O-Trays (image 7).
When readying a case to be paired with an album you don't have yet, just swap the tray for a double tray. That's what I did with my Shine - The Hits CD, which will be paired with Thrive as soon as I get it.
Step 4: Tranfer the U-card and cover note.
This is the part where you'll have to determine which U-card goes in first.
The flat part of the U-card, between the folds, varies in width from case to case. The narrowest one should go inside. Sometimes, they're the same width. In that case, you choose.
A wider U-card won't lay flat in a narrower one, which can cause problems later.
Once you have determined which card is the narrowest, lay it upside-down on the table with one folded end off the table (image 2, unless you know a better way), then fold the end 180 degrees (image 3).
Repeat for the other end. The card should now be "inside out".
Lay the U-card on top of the other one in CD case 2.
Now it's time to transfer the cover note.
Pull it out, flip it over (image 4), then slide it in on top of the other cover note (image 5).
Add the now-empty CD case to your Stack-O-Empty CD Cases (image 6). You may need some of those later to replace damaged cases, especially when dealing with damaged double CD cases you may already own.
Step 5: Double tray time!
It's easier to put the CDs in the tray before putting the tray in the case, so
Pick which CD you want in the bottom, and snap it in the bottom of the CD tray (image 2)
By doing it this way, you'll find out if the tray is defective. (image 1)
Flip the CD tray over and snap the other CD in (image 3)
Insert the tray in the case with one corner of the tray set in the case (image 4),
make shure the U-card does not rise and get pinched between the tray and the case.
then snap the other corner down (image 5).
You may have to nudge the tray horizontally to get the snaps to engage.
Flip the tray out and in to make shure it functions as intended.
Step 6: Take it for a test drive.
If it doesn't close, check the cover notes. They may have slid too far in, getting pinched between the lid and the tray, or if they're not slid in far enough, they may act like a 'foot in the door'.
Sometimes, the tray doesn't seat completely in the case. If that's so, just push it in.
If the combined thicknesses of the cover notes is too great, the case may close hard.
Repeat for the next band, artist, or category.
Step 7: What to with the empty cases and trays
Obviously, anything that's cracked, broken, scratched up, malfunctional, or otherwise damaged, should just be tossed into the rubbish bin.
Keep a few just in case, eg. if a borrowed CD's case gets damaged while in your possession.
Now, about the rest:
Sell then in a yard sale, or give them away. Better to give it to someone that can use it, than trash it.
Or come up with nifty little idea worthy of its own Instructable.