If I had a Linode that connected to another non-Linode data center using OpenVPN.

Could I setup static routes on other Linodes in the same data center as the Linode connected to the VPN to route packets for the VPN remote subnets over the internal network?

Is this allowed?

It most likely won't work unless you tunnel the packets, somehow. Packets leaving your Linodes are filtered by source IP address. Since you've already got an OpenVPN infrastructure going, you could use that across the internal LAN as well. (Bonus points for building a self-healing mesh network for efficiency and resilience.) Or, GRE tunnels ought to work, and will probably be easier.

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This definitely possible with ipsec vpn or openvpn tunnel. You essentially configure it to send the internal ip address over the internet to the other data center and vice versa. I would recommend openvpn to novice, and ipsec if you are more familiar with it. Ipsec is a little more tricky to setup but would be slightly faster.