Configuring another interface via DHCP

I'm setting up a cluster of machines, each of which is connected to a
private network on eth0, as well as to other networks on different
interfaces. I would like all the interfaces to be configured
automatically, as the machines are net-booting from a common image, but
the only DHCP server is on the private (eth0) network.

It would be convenient to store the configurations for all the machines'
interfaces in one DHCP database on the server on the private network. Is
there some way to get a client like dhcpcd to configure an interface other
than the one on which the DHCP transaction takes place?

Any help would be appreciated.

--
Ed Swierk
eswierk-(E-Mail Removed)