I think your going to have problems doing this.
You say there are multiple websites using the same IP address? Do all these websites need to be SSL secured? The problem is going to be that you will need a seperate IP address for each SSL website regardless of the SSL cert installed.
Or if you wanted to use just the one IP address, you need to offload the SSL onto a load balancer, or a seperate service (such as the IIS ARR proxy) before passing the traffic unencrypted back to the webservers.
This is because the SSL traffic is encrypted, so IIS won't be able to read the header to see which website the traffic is destined for.
Otherwise, the process for generating a UCC cert is to request the usual CSR that you would do in IIS using the first DNS name, and pass this onto whoever is providing you with the certificate. They will then ask for the additional DNS names which you can supply to them. Then the cert gets installed as usual.