Dns1.mydomain.com instead of dns1.dreamhost.com?

I have a shared hosting package with Dreamhost, and I have to enter dns1.dreamhost.com, dns2.dreamhost.com, and dns3.dreamhost.com as the DNS servers for all domains I would like to host on my account.

Can I add a DNS record to mymaindomain.com so for every new domain that I register, I will have to enter dns1.mymaindomain.com, dns2.mymaindomain.com, and dns3.mymaindomain.com instead of the dreamhost.com ones?

dns1.mymaindomain.com would possibly forward/mirror to dns1.dreamhost.com behind the scenes.

Is this possible? If yes, how can this be done?

Any help would be greatly appreciated.