Possible to reverse proxy WP multisite to a separate server with NGINX?

I’m not sure if it works first time, but lets try.

server {
    server_name mydomain.com www.mydomain.com;

    root /var/www/html/wordpress/mydomain.com/wordpress/;

    # The "^~" modifier makes this location to take priority over regex-matched locations
    location ^~ /oldsite {
        proxy_pass http://my.old.ip;
        proxy_set_header Host $host;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto $scheme;
    }

     index index.php index.html;

     location /wp-content {
        root /var/www/html/wordpress/mydomain.com/;
    }

    location ~ \.php$ {
        # This rule now goes here, "last" changed to "break" to not leave this location after rewriting URI
        rewrite ^(/[^/]+)?(/.*\.php) $2 break;

        fastcgi_pass 127.0.0.1:9000;
        #If a file isnt found, 404
        try_files $uri =404;
        #Include Nginxs fastcgi configuration
        include /etc/nginx/fastcgi.conf;
    }

    location / {
        # Two other rewriting rules goes inside the root location block to not interfere with "location ^~ /oldsite { ... }"
        if (!-e $request_filename) {
            # Don't use $uri here, see https://github.com/yandex/gixy/issues/77
            rewrite /wp-admin$ $scheme://$host$request_uri/ permanent;
            rewrite ^(/[^/]+)?(/wp-.*) $2 last;
        }

        try_files $uri $uri/ /index.php$is_args$args;
    }

}

I comment the changes I’ve made to your config.