On the Standard Horizon HX870 DSC which I own it is possible for the user to re-programme a new MMSI number by use of a password obtained by emailing the manufacturer.
The process is detailed here:
Reset of MMSI for DSC Radio by End User - CONTINUOUSWAVE
I don't know if there is a charge for this or if they limit the number of times per set; I would also hope they check for valid ownership details to prevent this happening if the unit is stolen.
The linked thread also goes on to discuss some other units where this is possible.