There is a solution that you exactly looking for.
It is a chat plugin for BuddyPress and WordPress.
This chat has three basic feature such as:
Text group chat between users
Text private (one-to-one) chat between users
Online chat support (chat with customers)
Besides these functions, the ImbaChat has also:
Sharing files (any type of file)
Video chat (group and private)
The ImbaChat basic functions are free. Pricing for the additional features is from $4.99 to $19 per month. Easy and quick installation on BuddyPress. Full integration with the user base of your website.
Visit the official website of the plugin to learn more.
Hello, our team has developed the chat plugin for BuddyPress with many useful functions, such as: group chat, emoji, sharing files, online consultant.
There is also function of private chat between users.
The Basic tariff plan is free without limits.
I would you recommend a new chat plugin ImbaChat. It has function of live chat between users and group chat. Now, the Basic tariff plan is free. It includes all these features + online chat support feature.