Nope, not likely for you my friend.
If you happen to be an authoritative server, which is highly unlikely, you can use dig to determine the primary name server and then request a zone transfer query (axfr) ...
dig @ns.primarynameserverhere.com example.com axfr
... and then this will only work if the primary name server you query is configured to allow axfr requests from your
IP address. And unless your IP address has been configured as a secondary for the domain ... well, this ain't gonna happen, cap'n.
All these safeguards are in place so the only way to determine is to have access to the zone file or else query for the cname, one by one. And if you attempt this one-by-one query process automagically via a script, it is going to look like you are being quite naughty so my recommendation is to simply ask the domain manager for a list of the subdomains or a printout of the zone file.
I just realized that you may be asking about other
domains on the same server ... I thought perhaps you were asking about subdomains for a given domain name. A quick search on your favorite search engine will turn up plenty of options for reverse IP lookups.