Unlike the Japanese version of Fire Emblem Fates, you won't be able to "pet" your fellow soldiers, Pokemon Amie style. But that's OK. You still get something! Slight spoilers for Fire Emblem Fates here!
Basically, the way it works is, once the player gets to chapter seven of Fire Emblem Fates, the game introduces its new castle-building mechanic. As you've probably heard by now, within Fates you get a special space which you can use to gear up, rest and customise to your hearts content. Think of it like an upgraded version of Awakenings' barracks.
One of the amenities provided to you in this locale is something called "private quarters". It looks like this:
Once inside, you have a couple of options:
If you invite someone over, you are treated to a close-up of that character's 3D model:
In this case, I invited Felicia over to my private quarters. She said "Thanks for inviting me over...and for not asking me to clean your room." And that was that! It was a nice moment, and Felicia left happy:
Our bonds were strengthened, no unnecessary touching required. Cool.
At first I was bummed that Nintendo was doing away with the petting mini game -- I'd heard that the Japanese version used special binaural audio to enhance the petting scenes, making it seem as if characters were sultrily speaking straight into your ears. It's a technique commonly used in dating sims, and I was curious to see it in action in Fire Emblem, a franchise with awesome characters.
This is still good, though. English speakers still get the related content, without having the game veer into potentially uncomfortable territory regarding character consent in these scenes. Great!