The discussion so far has only been in regard to an MMSI. There is more to being a citizen of the USA and operating a radio in a foreign country than the MMSI number of a DSC radio.
In brief, in the USA you need a station license for a radio transmitter, unless that category of radio transmitter is "licensed-by-rule." The licensed-by-rule ship station license is available only to ships who are voluntarily equipping with a radio, AND the ship does not visit foreign ports, AND the ship does not make international communications, AND the radio is a VHF Marine Band radio (or AIS transponder).
For the actual federal regulations see
https://www.law.cornell.edu/cfr/text/47/80.13
Also, generally you need radiotelephone operator's license to operate a radio transmitter. For recreational boaters with voluntarily-equipped VHF radios, the requirement to obtain an operator's license is waived, but you still must follow the rules.
If you are an American citizen and you are in a foreign country, you do not automatically have the privilege of having a radio station and operating it. You may be granted those rights if there is a reciprocal licensing agreement between the USA and the foreign country. These reciprocal licensing agreements recognize the licenses you have from the USA and permit you to operate the transmitter you have in the foreign country, but according to their rules.
Of course, if you are a recreational boater with a licensed-by-rule transmitter and no operator's license, then you really do not have any license for reciprocal authorization in a foreign country. This is the basis for the FCC rule that requires boaters who visit foreign countries to have an FCC SHIP STATION LICENSE for their transmitter and to have an FCC OPERATOR'S LICENSE to operate it.
An FCC SHIP STATION LICENSE now costs about $220 for a ten year term. You just apply for the license--actually the hardest and most difficult part of the process. During the application for an FCC SHIP STATION LICENSE you can also ask for a maritime mobile service identity (MMSI) at no extra cost. With the ship station license you will also get a RADIO CALLSIGN.
You will also need to obtain a RADIOTELEPHONE RESTRICTED OPERATOR PERMIT, the lowest category of operator's license that will permit you to operate a VHF Marine Band radio with an official license. This license is good for the LIFETIME of the licensee. I don't know the exact cost at present; it used to be about $60. To obtain one, you just apply and swear and avow you know the regulations and will follow them.
The cost of these licenses from the FCC are based on two fee categories: administrative fees and regulatory fees. The FCC fee schedule changes every few years.
USING EXISTING MMSI
As far as I know, if your boat already has an MMSI issued by a licensed-by-rule private agency (like BoatUS), you cannot use that number with the FCC SHIP STATION LICENSE. You must get a new MMSI, one that ends with a zero.
Assuming you comply with all of this, you will then have the unfortunate problem of having a DSC radio that probably cannot be re-programmed by you in the field to a new MMSI. You choices then will be:
--send the radio back to the manufacturer and have its MMSI changed or reset; this will probably cost you a fee and shipping, or about $50;
--buy a new Class-D DSC radio, which is probably better than the one you have, for a cost of about $120.
RE INFORCEMENT
I have been boating in Canada as an American citizen on my recreational boat since 1986, or 33-years. During that time no representative of any Canadian agency has ever asked me to produce a SHIP STATION LICENSE or an OPERATOR'S LICENSE. However, my boat does have an FCC ship station license, and I do hold a radiotelephone operator's license. (I actually have a much higher grade operator's license than the minimum required.)