I found this command from CLI reference guide 'server_nsdomains' which seems to have this capability as the guide explains but VNX is still limited to only 3 domains as a whole no matter how many VDM's you have running. So the final answer is still a NO to the actual question
Hello,  I have a VDM built on a VNX 5800 data mover running on File OE 8.1.21-266. Both the VDM and server_2 are on same domain but is it possible to setup different set of DNS servers on VDM because we wanted to run a test? I tried running server_dns and got the message "Error 4035: : server_dns : operation not supported for VDM" 
VNX: Change DNS on VDM