Take a look here:
https://www.boatus.com/MMSI/
This is for vessels not calling on foreign ports, like Bahamas, BVI's , etc. etc. You can edit the MMSI to change your and your boat's info., transfer the MMSI to a new owner, add additional radios, like a HandHeld, SSB, AIS, etc. to get an additonal MMSI. It looks pretty straightforward and very flexible.
If you do call on international ports you are required to get a federal FCC radio license, and a new MMSI along with that:
"If your vessel requires licensing by the FCC after you have obtained an MMSI number from BoatUS, Sea Tow Service, Shine Micro, Inc., or United States Power Squadrons, that MMSI number cannot be used during the application/licensing process when you file FCC Forms 159 and 605 with the FCC. MMSI numbers issued by other authorized entities are valid only for ship stations that do not have FCC-issued licenses. Since the ULS will not accept the MMSI that was issued by another entity, you should not enter anything on FCC Form 605, Schedule B. Leave the field blank and the FCC will issue you a new MMSI number."
But, again, changes seem to be provided for:
"Making Changes During Your License Term
If you change your mailing address, legal name, or ship name, you must complete FCC Form 605 for Administrative Update. There is no fee required. No action is required when you add or replace a transmitter that operates in the same frequency band.
Send your completed form to:
Federal Communications Commission
1270 Fairfield Road
Gettysburg, PA 17325-7245"
So, if you operate domestically, you can avoid the gov't, deal with Boat/US or SeaTow, etc. websites and pretty easily deal with even multiple MMSI's. If truly blue water cruising, well, like the USCG itself, ya gos to deal with the Feds and their forms.