There is one handheld portable VHF/DSC/GPS out there than can have the MMSI changed without being sent back to the factory. It's the
Nautilus Lifeline Marine Rescue Radio. It's an emergency VHF/DSC radio originally designed for divers and not really intended for routine communication. It's a fully functional VHF with DSC and builtin GPS
www.nautiluslifeline.com See the bottom of the SUPPORT/MMSI INFORMATION page for how to easily change the MMSI.
I own a Nautilus Lifeline and have witnessed one in use to recover a lost diver in the open ocean. They are very waterproof and much smaller than the typical VHF/DSC/GPS units. The smaller size makes it much easier to attach to your lifejacket, etc.
Regarding Starbuck's (Tchoupitoulas') question, the Nautilus Lifeline website has instructions on how to get an MMSI for a "Portable Diving VHF w/DSC." And states that "You will be able to login and update the registration at any point to include current locations should they change periodically."
Tom Patterson
Dazzler