Suggestions: (Diplomacy adjacent - worth a shot)
King and Vassal both:
1.) Add a chamberlain that you can hire for a weekly fee to your court/residence who would handle the acquisition of basic to extended equipment (clothes, armor, weapons, horses etcetera) for his lord and his lord's companions. For the service he could be paid a fee that of a small to large percentage above whatever you requested at it's highest retail price with no trade bonus. The chamberlain could also hold your gold (and perhaps give gold weight to make this more enticing) and manage your finances. He would also in the place of a wife acquisition food or perhaps delegate this to him entirely, as it was more his duty than a noble lady's.
The chamberlain would soon appear the moment you have a Manor (a bit more difficult), Castle or Town. The manor would make realistic sense, but feasts cannot be held in manors, manors have no storage and really no space for him to reside.
With that done you would also need to add this to the retainer of NPC lords as well to reside in their households and courts for the sake of general game-play.
A chamberlain, anyway, is the officer in charge of running a household (wardrobe, finances, larder and so on) for his noble blooded master.
2.) Add the Seneschals to the game. There is currently one for each castle and town that are not implemented in the game but exist in the text files, and who have some dialogue lines already prepared but no overall purpose. You could make them hire-able by the player to give more precise details on tax and tariff revenue and perhaps reduce rent waste when controlling more than four fiefs. He would also handle feasts in stead of a wife, or perhaps delegate this to him entirely, as it was more his duty than a noble lady's.
For the A.I. you would likely want to limit them their number to the number of lords, rather than the number of castles and towns. Since it fell more to a constable or sheriff/baliff to watch things locally.
Seneschals were like Stewards, typically the head minister of a household, above the chamberlain who handled taxes and rent revenue payments and other domestic administration for a noble or royal lord.
To my understanding they were similar and sometimes synonymous to a chief minister/chancellor. However monarchs typically had one with a fluffier title (chief minister/chancellor) with more responsibilities, and thus one's existence here does not discount the other.
3.) Add Constables (Towns) and Sheriffs (Castles) to the game for AI and player alike, general purpose being fluff and hire-able by the player to increase loyalty and or production perhaps? They could take to the battlefield and possess better equipment in defensive sieges than the average knight.
Constables would function alongside the Guildmaster in towns, the latter who is technically like a mayor at present, but is seen as a local head of the guilds. Thus leaving room for the more appropriate 'constable.' Who is more of a law-enforcement and sometimes military official, also known to be assigned to care-take of fiefs when their owner is away.
To my understanding sheriffs are similar, but function on a more local level.
King:
1.) Add a weekly fee for your minister of around 18 denars a week, which said amount is historically accurate (roughly).
2.) Add a Private Secretary to your court, hire-able by the player for a weekly fee. He would handle all correspondence, gifts (instead of your wife, which is 'typically' not her duty, at least a queen) and letters/orders to other lords, and so on. So instead of looking for a specific lord by traveling around, or holding a feast for the entire realm to talk to one, you can send him a command or summons from afar.
Naturally, other A.I. monarchs would also have private secretaries for the sake of immersion. Time would typically be three days on average like a companion emissary.
Addendum/Edit:
3.) Your minister can raise troops for you, initial payment for each soldier is increased, nearby fiefs are depleted of recruits, size of effect dependent on how many you request. How many you can request is dependent on the size of the realm. The larger the request the more time it will take. Troop type could be a mix of whatever lands you hold, or perhaps a choose once and forever live with what you chose troop tree (swadian/vaegir etcetera).
General Game-play/Fluff:
Give NPC Monarchs and Successful Claimants a Minister (fluff).
Summary:
Basically, courts and households should be more crowded and interesting.