What’s the purpose of a second major?
The way your question is phrased, it sounds as if you want a double-major, just for the sake of double-majoring, but want as much overlap as possible to minimize the number of classes needed.
First of all, most universities limit the number of classes that you can “double-count” toward two majors, or toward a major and a minor. Beyond that limit, additional overlap will not benefit you.
Secondly, it’s not essential to double-major at all. Looking for the most convenient or efficient double-major is not really the point; the point is, what knowledge and skills do you want to acquire? You could be a history major with a minor, or even two minors, rather than a double-major. You can have just one major, and choose other classes that interest you without regard to major/minor requirements. The decision process should begin with what interests you and what preparation you may need to pursue those interests in the future.
Here’s a minor that could be both interesting and useful for a history major: Undergraduate Minor - Digital Humanities - UCLA
And here’s another:
http://statistics.ucla.edu/undergraduate/social-data-science-minor/
and another:
GIS&T Minor | Geospatial @ UCLA
Is there a particular part of the world that you’re interested in? A minor or double-major in a world language or a “studies” field focusing on a particular region could blend well with a history major.
Or perhaps you’re interested in how the arts reflected and influenced the arc of history.
https://arthistory.ucla.edu/undergraduates-major-minor/#/minor-in-art-history
or
https://schoolofmusic.ucla.edu/academics/musicology/minor/
Or, if you’re interested in a particular driver of historical events, consider studying political science, public affairs, economics, religion, or even public health. This minor looks interesting as well: Program.::. UCLA Academics
There are many options. Better to focus on what interests you most - if that adds up to a second major, fine, but if it doesn’t, that’s fine too.