I have a Customer Community with sharing set up in a way that allows Community Users to edit their own Contact record. I am able to change every single field on the Contact record when logged in as a Community User, with the exception of one: Account Lookup.
I suspect this is a security precaution. Sharing Sets grant elevated access, and can work based off of which Account your Contact record belongs to. If you can change your Account, you get access to a different set of records.
Is this possible? If not, is there documentation that outlines why it isn't possible? I haven't been able to find anything.