I'm kind of new to carving so the answer is probably more obvious than I think. I'm making a large dome shaped cake. I'm starting with four 12" rounds stacked. From this, I'll carve the dome. I'll be using the cut off top corners for something else if you're wondering why I'm not graduating the size of the cakes I'm stacking.

My problem is that this will need some internal support as it will be 8" tall. So if I stack the four cakes with straws and cake board after the first two layers, how do I carve the dome shape with the cardboard there?

I though of stacking the cakes first, without support, then reassembling with support after it's all carved. But wouldn't adding all that filling (7 layers since I'll be torting the 4 layers of cake) and cardboard distort the lines of the dome?

When I see them carve on the cake shows, it looks like they are carving right through the cardboard. Can this be so? It seems a recipe for disaster to me.

I've only done this once, so I'm no expert, but how I did it worked for me. I carved a beach bucket out of four 8" rounds. I stacked cake, BC, cake, covered the top in a thin layer of BC, doweled for support (of course), and then put a cardboard round on. The cardboard was approximately the size of the circumfrence of my beach bucket once finished. So, I was carving from 8" down to 6", midway thru my bucket was probably 7", so my cardboard was 7". Does that make sense? Then I repeated the layers and started carving.

So, to make a long explanation short, my cardboard was about the size I expected that portion of the finished cake to be

Yeah, I wonder that myself...how do they cut through the cardboard unless the cardboard is soft from the cake, which to me would be problematic for the structure itself...even with dowels.
You know you might reconsider carving before torting and filling. Any gaps or additions can be filled with buttercream, or cake spackle (BC mixed with cake crumbs).

I most recently did a Barbie cake dress that was domed at the top...obviously not as large as yours is going to be, but I used a bowl to create the dome so I wouldn't have to carve. You might look around for a bowl that you could use as the top of the dome...if the base can be worked into the size you need that is.

on a couple Amazing Wedding Cakes episodes I've seen the decorators carve just the cake first, then torte and add support once they have the carved shape completed.

If it's a symmetrical dome, then you already know what size the cardboard needs to be. Use the correct size boards, so you won't have to cut them. In fact, they would probably be useful as guides while you're carving, you know when your knife nudges the cardboard that you can stop trimming cake.

The dome will not be symmetrical...more of an organically shaped, elongated dome shape. I won't really even know the exact shape until I work through the carving. So I can't pre-cut the cardboard to the anticipated size/shape. And the bowl's a great idea...but again, not in this instance.

I think I may revisit, as carmijok recommends, the stack, carve, disassemble then reassemble with structure and spackle.

Thanks for all the suggestions. I'll let you know how it went.