The closest you might be able to get is to do what Sega did with the Mega Drive/Master System and Master System/SG-1000 - which is basically have a Sega Saturn lying (mostly) dormant inside the same console case as a Dreamcast. But you'd need to find a way to switch from one to the other (The Mega Drive recognised the Master System converter and switch accordingly, but a mod likely wouldn't have that form of control) safely.
There are multiple issues in doing such a combi system however, some of which are;
- Disc Drive. Dreamcast and Saturn read different disc types. Saturn reads CDs, Dreamcast reads GD-Roms. The Dreamcast laser can read CDs as well, however if you use the DC's disc drive for both you'd need to find a way to get the Saturn to control the drive when it's active. It's likely possible, but it's way above my knowhow.
- Space. The Dreamcast is very snug inside it's shell, leaving the more plausible shell to be the Saturn's. However even assuming you can get the Saturn to read from the DC's disc drive, finding room for two motherboards will not be simple. The Saturn's power chip is a big, long one (the same size roughly as the Dreamcast's) so you could swap it out for a much smaller custom PSU, but it still wouldn't be enough space to house the DC motherboard.
- Heat. The Dreamcast runs loudly enough on it's own (though custom fans can improve this problem). Replacing the PSU can reduce the actual temperature inside the unit, but there's no fan holes in the Saturn system to begin with. You would need to place this, as well as ensure good airflow.
- Adapters. The Saturn utilises a card slot in the back for expansions such as the VCD card, and to replace the internal battery. The Dreamcast needs a slot for the modem. Both of these (in the stock devices) would be at the rear-right of the units. Unless you do a full internal-modem using a Pi Zero W, you'll likely not get these to fit.
Controller Ports. The Mega Drive, Master System and SG-1000 all used the same controller port, making them easily accessed by successive machines. The Saturn and Dreamcast both have custom controller ports, and the Dreamcast's require extra power to support the rumble pack, microphone and VMUs. There may be a way of getting the Saturn to read the DC's controllers, but somehow sharing the same controller chip might not be possible.
I don't think it's impossible to make a Frankenstein console like this, and it would be in keeping with Sega's historical backwards-compatibility. However it is impractical, and requires owning a Saturn and Dreamcast anyway. This also wouldn't allow the Dreamcast to play Saturn games, simply allowing both consoles to share common ports and drives.
But that's as much as I can think of for the idea.