How many domains can be bound with one SSL certificate?

There are multiple certificate types.

• You can have a wildcard cert *.domain.com which is valid for all subdomains.
• You can have a single-name cert host.domain.com which is only valid for this host
• You can have a multi-name cert host1.domain1.com, host2.domain2.com, this is called a SAN (Subject Alternative Name) Certficiate. They are often called "UC-Certificate" by cert vendors.

I'm not sure where the technical limit is on a SAN cert, but it's certainly more than 10 names.

If they are truely unique domain names, you can get a SAN (Subject Alternative Name) certificate. Most vendors will let you put about 40 domain names on one cert. If they are sub-domains, a wildcard cert is the way to go. For each of tjose options you only need 1 ip as the cert is valid for all listed domain names.