I have a "catch-all certificate" that I would like to use on another server that resides in another VM. How can I achieve this? I haven't seen any docs that explain otherwise.
Yes. You need to export the certificate with its private key and then import it on the other server.
How you do that depends entirely on the OS / Webserver that you use.
Also, make sure that your certificate provider allows the installation and usage on multiple servers.