"no rules" Michael. give it a go and see what it sounds like...
No reasons not to. CBGs can be odd ducks for tone. I have had fiber board boxes sound good and thin wood boxes sound not so good. They are like Forrest Gump's box of candy. You don't know what you get until you bite into it.
Timothy Hunter has already shared a mindset that will serve you well -- "no rules." Not that you did in your post, but don't put limits on what's possible. Even if your plan doesn't work out as... well... planned, you still learned something valuable and hopefully had a good time doing it.
And Uncle John has served up the best advice I've read on this subject. Boxes, and nearly all things cigar box guitar-related, are like a box of chocolates. While you may have a good idea of what results to expect from known steps, you never really know until you try.
Have fun with it, Michael, and whatever you build will be worth the effort.
I've actually in the middle of trying this very thing! I came across several identical cigar boxes, but they weren't as deep as I'd like them, so I cut out both bottoms up to about an inch from the sides and glued and clamped both together (see photo). After it dried, I cut out the rest of both bottoms as close to flush with the sides as I could get. Now I have a deep(er) cigar box that opens on both the top and bottom. Acoustically, it seems fine, and it does seem deeper and has more bass when I thump it now. I'm still working on the neck to attach and finish the thing, but I've been ill and it's cold in my shed.
I'm sure I'll try this again with other duplicate boxes - and maybe with some that are differently shaped. Also, I may try gluing the top to a bottom to see if the resulting tone is better. As they say, you gotta try these things yourself to see what really works for you!
It is a bonus, you have a bigger chamber, a bigger chance to be louder, as others have said, sometimes the volume and sound defies logic, but , bigger is a better chance than smaller.
I'll certainly let you know how it turns out.. but I wouldn't be too sure who'll finish first! It's been quite the lazy year for me as far as CBG's go.
I've done 5 builds using the sandwich method great way to get a better sound from the thinner boxes , I've a few thinner boxes here I'm planning on doing them the same way ..have fun