Fourth Officer
Fourth Officer is a rank used by the Royal Manticoran Merchant Marine.
Honorverse
In the Honorverse, the Star Empire of Manticore uses the rank of Fourth Officer as the more junior of the two individuals holding a Third Officers Certificate of Competency on freighters that carry two Third Officers. On passenger liners with multiple people having billets that require at least a Third Officer's Certificate of Competency, as seniority goes down, their number goes up. Therefore, a passenger liner with 6 junior officers could have a Seventh Officer. Other star nations only use the rank of Third Officer with a number after it. Thus Third Officer number one, Third Officer number two, etc.
TRMN
In TRMN, a Fourth Officer is a merchant marine deck officer who has 1) completed their Fourth Officer exam (Line track) or Spacer IV exam (Staff track), and 2) has served as a C-8 (Spacer VI, Certified Bosun, Technician VI, Chief Steward, Senior Sick Berth Attendant) for nine months Time In Grade. At this point they are eligible to be promoted to this rank by their Commanding Officer (military) or Master (merchant marine) of the chapter. They can also be promoted, regardless of Time In Grade, during a ship upgrade if the ship needs more officers.
Real World
In the real world, a Fourth Officer is the designation given to the next junior Third Officer on ships with more than one Third Officer. The term is primarily used in the UK and Commonwealth countries. If there are more than 2 Third Officers, each more junior billet will go up by one number. So a cruise ship with 6 junior officers could have a Seventh Officer.