None of what you describe should be necessary nor require using layout mode.
Your data model should be one of the two:
Companies::__pkCompanyID = Contacts::_fkCompanyID
In which case, moving a contact from being associated with company A to being associated with company B is a matter of assigning company B's ID (value of __pkCompanyID) to the contact's _fkCompanyID field. This would be a data entry task done in Browse mode.
or you might have:
To enable one company to have multiple contacts but still be able to link a contact to more than one company. In that case, the same kind of data entry update is made, but to a record in Company_Contact rather than Contacts.
Always appreciate your fast and useful answers.
You're right and I might explained it, a bit too fast.
My data model is looking like the first you describe; Companies-----<Contacts.
Although your right, this should be entered in Browse mode, I don't want my colleaguesto change it 'that way', since they're not familiar with FileMaker, Relationships and therefore might use it in a wrong way.
Therefore I would like a button, if possible, which just pops up and ask the user "Change ID to ID"
Whether you pop up a new window, a popover or just use your current layout, switching a contact from company A to company B still comes down to using a value list of company names where you edit the _fkCompanyID field by selecting a different company from the value list.
You can put that field into a popover or a new window if you want, but it's the same data entry process.