It is
possible, but extremely difficult to set up, so unless you have a lot of networking and scripting expertise, you probably can't do it.
However, you should read
Tunnelblick and VPNs: Privacy and Security, which explains what VPNs can and cannot do to protect your privacy (tldr: not much, depending on who is trying to track you). (Everything in that article applies to multi-hop VPNs, too.)
It requires customized "up" and "down" scripts to handle DNS and routing. They would be extremely complicated to set up, especially if you have not set up each of the VPNs yourself (which seems to be your situation), because you can't rely on any specific networking setup (e.g., IP addresses and subnets) for either VPN.