Allowing client domain to point to my domain

Question

I'm currently using Plesk which is running a nodejs app. I'd like to enable users to point their domains at mine eg:

client.clientsite.com -> client.mysite.com

My extra nginx file looks like so:

server_name *.mysite.com;
location ~ / {
    proxy_pass http://localhost:3000;
    proxy_set_header Host $host;
    proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
    proxy_set_header Host $host;
    proxy_http_version 1.1;
    proxy_set_header Upgrade $http_upgrade;
    proxy_set_header Connection "upgrade";
    proxy_redirect off;
}

I've tried:

server_name _;

But this does not work, this also breaks the subdomains for mysite.com. It does kind of work with:

server_name *.clientsite.com *.mysite.com

But this would not be a viable option as the website grows. The *.clientsite.com also ends up showing www.mysite.com instead of client.mysite.com

The SSL is all setup via cloudflare and works fine, its just this nginx problem which I cannot get my head around.

Thanks