Eddie sez:

Losing your ability to keep the airplane precisely on altitude is becoming a bigger deal every day, as the skies are becoming more tightly packed. Because each situation is likely to be unique, there are no cut and dried rules that always apply.
You should also refer to: Special Procedures for In-flight Contingencies in Oceanic Airspace.
Everything here is from the references shown below, with a few comments in an alternate color.
2021-02-26
[ICAO Doc 9574, ¶5.1.1 h)] The following contingency procedures should be adhered to after entering RVSM airspace:
These procedures are given in ICAO Doc 4444 and are provided here: Oceanic Contingencies.
North Atlantic loss of RVSM procedures are in compliance with ICAO procedures, given above. ICAO NAT Doc 007 provides a few additional procedures.
[ICAO NAT Doc 007, ¶9.1.7] Most flights will approach the NAT HLA through European or North American RVSM airspaces. It is therefore expected that continuous monitoring of the serviceability of the aircraft’s height keeping systems will have been undertaken. Nevertheless, in view of the significant change of operating environment (i.e. to indirect surveillance and communications) it is recommended that a final confirmation of the aircraft systems serviceability is performed immediately prior to entering the NAT HLA. Check to ensure the two primary altimeters are reading within 200 feet of each other (or lesser value if specified in your aircraft’s flight manual). Conduct this check while at level flight. You should also note the stand-by altimeter reading. The readings of the primary and standby altimeters should be recorded to be available for use in any possible contingency situations.
[ICAO NAT Doc 007, ¶9.2.1] The following equipment failures must be reported to ATC as soon as practicable following their identification:
The basic general procedures are outlined below. Consult AIPs, Jeppesen State Pages, and ICAO Document 7030, Regional Supplementary Procedures, for regional differences.
Portions of this page can be found in the book International Flight Operations, Part VI, Chapter 4.
ICAO Doc 4444 - Air Traffic Management, 16th Edition, Procedures for Air Navigation Services, International Civil Aviation Organization, October 2016
ICAO Doc 7030 - Regional Supplementary Procedures, International Civil Aviation Organization, 2008
ICAO Doc 9574 - Manual on Implementation of a 300 m (1,000 ft) Vertical Separation Minimum Between FL 290 and FL 410 Inclusive, Second Edition, International Civil Aviation Organization, 2001
ICAO Nat Doc 007, North Atlantic Operations and Airspace Manual, v. 2021-1, applicable from February 2021
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