As long as the CN in your certificate reflects the domain your requesting and the server knows about it, it should work.
make a csr for "cp.anotherdomain.tld", send it to your ca and use the key in your vhost for "cp.anotherdomain.tld".
an ssl certificate costs like 12EUR for 1 year, so you can just "try" ..
it's not that they cost a fortune
Remember that when you buy a wildcard this works: *.domain.tld
but this won't: *.*.domain.tld