Can I have 2 sets of name servers for one domain? i.e. If the sub-domain is not found one set of name servers then it checks the next set of name servers?
Sort of, but depending on your needs it may or may not work the way you want it to.
The purpose of having more than one nameserver on a domain is redundancy, if there are multiple then each nameserver would be expected to contain the same records as its peers.
That being said, you can create an NS (or multiple NS records) so that a subdomain and its children would be handled by another set of nameservers.
It would look something like the following...
Primary nameserver(s) for the domain (let's call them ns1.foo.com and ns2.foo.com, and let's say the domain in question is example.com):
. A 184.108.40.206 www A 220.127.116.11 sub NS ns1.bar.com sub NS ns2.bar.com (other records)
Sub nameservers (ns1.bar.com and ns2.bar.com):
. A 18.104.22.168 www A 22.214.171.124 (other records)
All name resolution requests will initially go to ns1.foo.com or ns2.foo.com. If the name to be resolved is
*.sub.example.com then the first set of name servers (
ns*.foo.com) send the request on to
ns*.bar.com for resolution.