Hello,
There is no build-in feature to add more fields. Instead you need to customize chat application to have the extra fields, then you can insert the collected data to CAD (Contact Attached Data) which can then be displayed at Communication Panel Extension Area.
For more information about customizing chat client refer to: Contact Center 365 Visitor Client API
For CAD please find setCad function. One handy feature you could utilize for collecting phone number or any other information is interactive chat templates where you can do forms and buttons.
What comes to mandatory fields, the same applies. Meaning that configurator doesn't provide the option, but requested can be customized to the chat client application.
In general the recommendation if possible is to insert customer identification details from webpage to CAD in case customer is authenticated. Same applies also to phone number if website already knows it.
BR,
Jukka
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