Multiple sites one theme

I have a health care directory website, so far the whole website is dedicated to one city, however, I need to expand to a different city and I want to use the exact same theme.

I was wondering if there’s a way both wordpress sites could use the same theme (same location) that way when I have more than 10 cities in different wordpress sites I only have to update 1 theme instead of 10.

I hope I’m explaining myself ok, heres an example:

3 different websites with 3 different wordpress installations:
mywebsite.com/newyork
mywebsite.com/losangeles
mywebsite.com/phoenix

Is there any way I can have (location doesn’t matter)
mywebsite.com/myTheme

So my websites can share a single theme.