It depends. For Stack Exchange: yes.
When you write something, you own the copyright, and have the right to do whatever you want with it (from a copyright perspective at least).
When you post something to some site, you usually give a license to use that material on that site, through the terms and services, or you transfer the copyright to them.
If the terms are to transfer the copyright to them, you no longer own the copyright, and you can't grant additional licenses.
If you grant them a license, it's either an exclusive license, or a non-exclusive license. If it is an exclusive license, you can't grant anyone else a license anymore.
If it is a non-exclusive license, you may still dual license your content, and make it available under some other license as well.
In the case of Stack Exchange, the terms read
You agree that all Subscriber Content that You contribute to the
Network is perpetually and irrevocably licensed to Stack Exchange
under the Creative Commons Attribution Share Alike license.
This means it is a non-exclusive license, and you can release your content to others under a different license as well. This seems to be the most common scenario for other sites as well, but you should always double check.
Note that this doesn't override the license. You are dual licensing your content. Per the terms and services, you have no choice but to license your work under CC-BY-SA. But you have no restriction to also license it under a different license of your choosing.
These licenses don't have to be compatible. Anyone can choose under which license they use your work, the standard StackExchange one (CC-BY-SA), or another you offer personally.