Is it possible to have a fastcgi_cache_path for each website / virtual host?

You can define multiple cache paths in the nginx http context:

fastcgi_cache_path /var/run/nginx/cache/site1 levels=1:2 keys_zone=SITE1:100m inactive=1w;
fastcgi_cache_path /var/run/nginx/cache/site2 levels= keys_zone=SITE2:123m inactive=60m;
# other fastcgi_cache_* settings here or in your servers/locations

server {
    server_name site1.com;
    # blablabla

    location ~ \.bla$ {
        # blablabla
        fastcgi_cache SITE1;
    }
}

server {
    server_name site2.com;
    # blablabla

    location ~ \.bla$ {
        # blablabla
        fastcgi_cache SITE2;
    }
}

My nginx:

nginx -V
nginx version: nginx/1.1.19
TLS SNI support enabled
configure arguments:
--prefix=/etc/nginx
--conf-path=/etc/nginx/nginx.conf
--error-log-path=/var/log/nginx/error.log
--http-client-body-temp-path=/var/lib/nginx/body
--http-fastcgi-temp-path=/var/lib/nginx/fastcgi
--http-log-path=/var/log/nginx/access.log
--http-proxy-temp-path=/var/lib/nginx/proxy
--http-scgi-temp-path=/var/lib/nginx/scgi
--http-uwsgi-temp-path=/var/lib/nginx/uwsgi
--lock-path=/var/lock/nginx.lock
--pid-path=/var/run/nginx.pid
--with-debug
--with-http_addition_module
--with-http_dav_module
--with-http_geoip_module
--with-http_gzip_static_module
--with-http_image_filter_module
--with-http_realip_module
--with-http_stub_status_module
--with-http_ssl_module
--with-http_sub_module
--with-http_xslt_module
--with-ipv6
--with-sha1=/usr/include/openssl
--with-md5=/usr/include/openssl
--with-mail
--with-mail_ssl_module
--add-module=/build/buildd/nginx-1.1.19/debian/modules/nginx-auth-pam
--add-module=/build/buildd/nginx-1.1.19/debian/modules/nginx-echo
--add-module=/build/buildd/nginx-1.1.19/debian/modules/nginx-upstream-fair
--add-module=/build/buildd/nginx-1.1.19/debian/modules/nginx-dav-ext-module

For anybody that followed https://www.digitalocean.com/community/tutorials/how-to-setup-fastcgi-caching-with-nginx-on-your-vps and is having issues setting up caching for multiple sites and is getting the error nginx: [emerg] "fastcgi_cache_key" directive is duplicate.

My solution was to place the fastcgi_cache_key "$scheme$request_method$host$request_uri"; within /etc/nginx/nginx.conf. As opposed to putting it in /etc/nginx/sites-enabled/vhost config which the above tutorial alludes to.

Hope this helps anybody else having a similar issue to me.