Basic question re Nameservers

Need experienced advice please.
Can I do this? Example:

Say my main reseller site is acme.com and is hosted with hosting Company A.

Personalized nameservers are set up as follows:
ns1.acme.com
ns2.acme.com

The domain name acme.com is set to those nameservers.

Now I intend to put my linux resold accounts on the servers of Hosting Company B and my windows resold accounts on the servers of Hosting Company C.

Can I set up personalized nameservers with Hosting Company B as follows:
ns10.acme.com
ns11.acme.com

And with Hosting Company C as follows:
ns20.acme.com
ns21.acme.com

My main site, acme.com will remain on the server of Hosting Company A.

(One experienced host told me you can't do this. He said the additional nameservers will not work because the domain name, acme.com, MUST point to it's own nameservers. Another host disagreed and said you can do it the way I outlined.)

Please advise. Basic question re Nameservers

Edited for clarity

 

 

 

 

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