Can you have NS records pointing to different providers?

You can add as many DNS servers as NS records for a domain, but they need to fulfill two conditions:

• They must host an authoritative copy of the DNS zone
• They must be kept in sync

So, no, you can't add any random DNS server around the world (such as Google's ones), because they would not be authoritative for that zone and so they could not act as DNS servers for it (unless Google actually is your DNS provider, which doesn't seem to be the case).

But you can add as many DNS servers as you want, as long as they actually are properly configured authoritative DNS servers for that zone; they can reside anywhere you want: on your network, on a cloud VM, on a hosted service... just make sure to keep them in sync, either using a standard primary-secondary zone setup or a replication system (such as Active-Directory-integrated DNS does).

Unless the nameservers provide authoritive answers to queries there is no increased resiliency. Make sure that every associated dns server hosts a copy of the zone on its own.