Short answer - Yes there is a limit. Only 10 officers are doing anything to help the city.

If you mean assignments like city repairs and land development- You can only assign 10 officers to city upgrades. Those are the assignments at the end of parliament. You will see it if you play as a ruler. If you have more than 10 officers, the ones not assigned will do nothing and not go up in rank. As a ruler, I try to limit the assignments to the best officers and only give them what they can get good results in, regardless of what they want to do. As an officer, I obviously try to get assignments I can accomplish. When possible get synergy with an officer that can help where you lack. So if you have no invent, find an officer that does and friend them so they can possibly help.

If you are an officer with that many officers in the city, your ruler should maybe march and expand. Not only are the officers just sitting idle, they are still collecting their stipend and drawing off the gold from the city.

You only need general you want to fight in battle going up in rank as they should be the commander of each unit, and the other are just deputy. Mostly these are for border city or connect to border city for reinforcement. If you assign an officer, they will be grey out as completed the mission or assignment for that parliament season.
Use them to plot against the enemy, diplomacy, buy/sell food, spy will also help them gain experience and grey them out as also complete the mission for that season.
Just do not keep too many officer in one city that isn't near border.