While adding a CNAME record, you may receive the following error:
You may not mix CNAME records with other records for the same name
You are receiving this error because a CNAME record is not allowed to coexist with any other data as per RFC1912 section 2.4.
If you are using cPanel and you are trying to add a CNAME record for the main domain (i.e. domain.com), you may receive the following error:
domain.com. already has a SOA record
This is due to the fact that a name cannot both be an alias (CNAME) and something else at the same time.
While other DNS servers may allow you to create an alias (CNAME) record and other record for same name but it is not at all recommended to do so. This can result into unpredictable problems because in some situations the CNAME record will override other critical records at the zone root level (NS, SOA etc.).