My understanding is that we are talking Boeing here, from the thread title and l agree that we are Europeans, so here is my take on it in this order.
Boeing and the FAA review the MRB revise it and this is then submitted to the aircraft types ISC (International Steering Committee), made up from the airline operators, Boeing and the authorities.
The ISC then meets and discuss the revision and either agrees, modifies or rejects the changes.
It is then signed of by the ISC chair (airline representative), the co chair (Boeing) and by the FAA representative on the ISC, it will normally also be signed by EASA.
The MRBR is then issued and the ISC co chair then passes it onto the department within Boeing who puts it into the next revision, or has been the case with both B757 & B767 over the last few years due to size and complex two revisions of the MPD.
Boeing issue revised copies of the MPD, 3 times a year, however the MRBR may go years between revisions.
Yes l agree the MPD is normally the document that we use for our AMS or AMP, but is the MRBR, plus Section 9 of the MPD which is the minimum that our local CAA office in the UK will accept.
You will struggle not to put all the MRBR tasks into you AMS or AMP, but you can leave out tasks from the MPD as many come from SBs or SILs that you do not have to carry out.
