Hi I have a client who has two websites with different web hosts, they want a blog that is shared between them, probably a k2 one.

The sites are already up and running but the blog has not yet been installed.

Can this be done with Multisite?

If you are using JMS Multisites, it is required to host the website on the same host and same account because the concept is to share the files on the disk and share the MySQL tables.

So if you are on different hosts this will not work.

In addition, the sharing is something that is decided when you create the website and you can not convert an existing website with shared extension.

So NO, not on different host and not on existing websites.

Otherwise, when on the same host with new website, this is possible with K2 but also with Wordpress MU