Is there a way to SELECT n ON (like DISTINCT ON, but more than one of each)

I have a table us_customers that looks like this (with hundreds of thousands of rows):

+----------+----------+
|    id    | us_state |
+----------+----------+
| 12345678 | MA       |
| 23456781 | AL       |
| 34567812 | GA       |
| 45678123 | FL       |
| 56781234 | AZ       |
| 67812345 | MA       |
| 78123456 | CO       |
| 81234567 | FL       |
+----------+----------+

… and I want to SELECT a sample of n customers from each us_state.

Is there a way to do that cleanly in PostgreSQL 9.3?

I can get one customer from each us_state easily with:

SELECT DISTINCT ON (us_state) id
FROM us_customers
ORDER BY us_state;

But if I want, say, three customers from each state, is there a way I can do this without running the same query multiple times?