Many players may already be aware of the fact that The Sims 4 lacks a story. So, here's some ideas of how to get a good story from a mod!
For starters, a simple mod that adds custom story-like responses in the notifications whenever a sim perform certain social interactions from the pie menu with the active sim. For an example, if your sim is on a hot date and the other sim flirts with you, the notification will say something like "You have beautiful eyes". It would work great during family dinners as well, when your sim uses the "Ask about day" interaction, the notification would appear saying "today I tripped and almost fell in a puddle". Another example is when a sim catches your sim cheating, they could say "How dare you!" after using the argue or slap interaction.
Another idea is making the 'Propose Marriage' and 'Divorce' social interactions autonomous and paired with a custom script that gives the player a dialog asking if you accept or reject another sim's proposal or divorce. The divorce will function like the 'Pay Bills' interaction on the mailbox. The initial divorce popup will include a warning of how much it would cost for a divorce. That way you can check your household funds before making a decision. If you accept the divorce, your sim will receive divorce papers in the mail that has to be signed (using the 'pay bills' animation). Once it's signed and placed into the mailbox, the divorce fee will be automatically deducted from the household funds. If your sim can't afford the divorce, the papers can't go into the mailbox until the funds become available. The breakup interaction could be made autonomous by default, while increasing the chances of it being selected when receiving betrayal buffs or having a negative romantic bar (why stay in unhappy relationship?).
Well, as simple or complicated as it may sound, I think these ideas could create some unpredictable and exciting gameplay.