Before MC starts a relationship with Kate: Talk to Rick in the morning about Kate, approve of his attempts to date her. During the serving game, talk to Rick when the two of you order drinks instead of MC, do this about 5 times and they should start being more flirtatious. After enough times, Rick will start visiting her in her room at the inn at 9am instead of in front of it.
If MC has already started a relationship with Kate: Wait until you have finished the preparations for Kirlic, do the scene in the barn and give Rick the signal 5 times, then talk to him in the morning and decide that he can start seeing her alone, then do the serving game with Kate talking to Rick 5 times for him to start visiting her room every other day.