Solution #1: Watch more Masterpiece.
Upstairs Downstairs: This started as a British drama in the 1970s, but in 2010, Masterpiece decided to continue the story. They made a three part mini-series that picked up the story of 165 Eaton Place with a new family and new servants, but great drama all the same! The new story takes place in the 1930s, and stars Keeley Hawes and Ed Stoppard, and Jean Marsh returns as Rose Buck.
Solution #2: Also written by Julian Fellowes
Julian Fellowes, who wrote Downton, has written for a lot of films and TV Shows. So if you enjoyed the excellent writing in Downton, you're bound to like these as well:
Gosford Park: This is a murder mystery set in the 1920s, and you'll like it, even if you're not a huge fan of murder mysteries. Because it's not really about the murder. Much like Downton, there are servants and masters, and it's fascinating to see their worlds collide. It's also very funny, and of course well written!