The ability to pet the dog or cat isn't cheap. *POSSIBLE SPOILERS*
http://www.nintendoworldreport.com/rumor/51759/tentative-plans-revealed-for-final-two-three-houses-dlc-packs-and-updates
A guide book published by Famitsu magazine in Japan and obtained by Fire Emblem resource Serenes Forest has allegedly confirmed the remaining DLC for Fire Emblem: Three Houses.
The free update wave 3 is said to include a new playable character (Jeritza, a Church of Seiros character), support conversations for Jeritza, new activities, and new online features of some description. Owners of the Expansion Pack will reportedly receive the recurring character Anna, a new paralogue with Jeritza and Anna, new monastery facilities, quests, costumes (Maid and Butler), the ability to play with dogs and cats, and the opening of the ingame sauna.
Nothing is listed in the free update for wave 4, but it will add "Abyss mode", four new playable characters original to the DLC, new costumes for the main character, and a whole host of new items. This will also include four new classes.
The third wave of DLC is due by the end of 2019, with the fourth and final pack to follow by the end of April 2020.