DBA owning another DBA
DBA is not a legal entity, but an "alias" for existing legal entity. For example, if you run your business as a sole proprietorship, the legal entity is essentially yourself, and you can register a DBA under that legal entity. If you want a second DBA that would again be registered as an alias for your sole proprietorship.
As such DBA cannot own another DBA, but a legal entity can register as many DBAs as necessary.