Sure, this is common.
You can also outsource it within your own country (I'm assuming US here, but Europe also qualifies).
The Atul Butte lab at Stanford uses this: https://www.assaydepot.com/
One of the interesting areas is "third-party multiservice". instead of acting as an exchange depot (send request to first service, get results back, ship resuls to second service, etc), the idea is to file an order with the first service, and chain the shipping to the next company, etc, so that only the finished product makes it back to the requestor.