Multiple Name Servers on a single IP [Would DNS Root Registry complain?]

Scenario:
I have a single IP, such as 1.1.1.1

I have a nameserver behind it, such as ns1.aaa.com.
I register ns1.aaa.com with my Registrar, and thus the root registry, thus holding my NS responsible for aaa.com domain.

Assume all of the above steps have been done CORRECTLY...

Problem:
What if I want the same host (i.e 1.1.1.1) act as ns1.bbb.com too? Assume that I do everything correctly (i.e my zone file and nameserver config are OK), would the Root registry not complain about the following situation?

ns1.aaa.com points to 1.1.1.1,
ns2.bbb.com points to 1.1.1.1

Is it possible?

Answer

No.

For a more detailed answer than "no", please do research on what glue records are and what role they play in the DNS. There is no central database of what nameservers are authoritative for all domains on the internet (unless you count the root nameservers, which don't work as you're describing), just glue records that are defined on a per-domain basis.