There is a not very well documented feature of iproute2 that allows to create additional virtual network interfaces, and assign different MAC addresses to them; you should then be able to run two separate instances of the DHCP client on each.
To create the virtual interface, do
ip link add link eth0 name eth1 address 00:11:22:33:44:55 type macvlan
Then try running the DHCP client.
It is legitimate to ask why you want to do this. If the machine has uses for many addresses with different roles, how will the machine figure which address to use for which role if they are dynamic ?
Also note that the ifconfig syntax with the
:0 suffixes is deprecated; with iproute2 you can simply use
ip addr add 10.0.0.1/24 dev eth0
ip addr add 10.0.0.2/24 dev eth0
and so on to assign several addresses to a single interface.