Yes you can, but why would you?
Firstly, you need to get this sorted on your own, and if your website has a database (most do), the process gets more complex.
Secondly, any domain or hosting issues and any web maintenance work you would need to handle yourself.
Do this only if you are absolutely confident you can manage and your new provider can provide all the support. If you are thinking of doing this to save on paying the annual or monthly web maintenance fee with us, the time and effort may cost you more than what you pay.