This is a really good question. I thought we had discussed this topic previously and I spent a while looking for where that was but I can't locate it now.
To answer this question requires answering a few other questions first, so let's look at the issues.
From a practical viewpoint, it's difficult to imagine why it's better to have one forum service the needs of four other distinctly different websites, each of which have their own rules, registration processes, content and activities. If each of these websites is distinctly different it would not normally seem unreasonable that each site should have its own forum dedicated to those separate purposes for which the sites were setup in the first place.
From a technical viewpoint, Kunena (like all other Joomla extensions) relies upon the Joomla user table in order to pair the messages with those who wrote them. This means that a user needs to register with the website where the Kunena extension has been installed before they can post messages on the forum (unless the forum allows anonymous/guest posting). If you have four websites, each of which has its own separate Joomla user table, the difficulty is to map those user accounts to the website that runs the Kunena forum. Most importantly, each website must use unique user identifiers so that messages are properly paired up with the authors.
One possible solution, to permit users of four different websites, to come together in one discussion forum, is to create a fifth website that runs the forum. Each of the four websites could have a link to the forum site. The practical problem, however, is that, when users are redirected to the forum site, people would have to be registered with that site and would have to login to use it. I can anticipate that your next question will be "how can I have a single user sign-on that's honoured across all of these websites?" I don't know the answer to that question, sorry.
So the difficulty lies not with Kunena but with Joomla.