Most battle facilities since Gen4 have implemented a Multi Battle mode where you can choose an AI partner to battle alongside you. I would add a friendship system to that. Your friendship with each characters would start at level 1 and could go up to level 5. There would be a hidden counter counting the amount of BP earned with a character as a partner, which would serve as the "EXP" for your friendship level with them (for example, 20 BPs get you to level 2 friendship, 50 BPs for level 3, etc.). Each time you go up a level, the character would ask you out on a "date" (it wouldn't be called a date but like "Hey, let's go to this cafe some time"). It'd be a short cutscene that reveals a bit more about the character or just a cute or funny scene like the Marnie smile scene, then at the end they gift you an item (like a bottle cap or something). I'd have some innuendos too (Not sexual ones but like, innuendos that your friendship is seemingly like a romantic relationship. For example, have the characters refer to you and them as "battle partners" a few times, but then as just "partners" too). When you reach friendship level 4 for the first time, a different character in the facility will tell you that in this region, battle partners who have forged an unbreakable bound usually go to Y location to make some promise or blablabla anything cheesy, but it's special because it's supposed to be for your ONE TRUE BATTLE PARTNER so you can only do it once. Then when you reach level 5 you're allowed to do it but only if you haven't done it with another character before, and the final reward is a baby of their signature mon and they say something like "I guess in a way this baby is like our child, haha, just kidding!"
It's not exactly a dating-sim but lets players get closer to their favorite character and their imagination would do the rest, and it ties the system into the rest of the gameplay as you raise friendship through battles and get rewarded items and stuff for it.