subdomain setup + domain mapping + a sub domani for the mapped domain

Is this possible?

Details

subdomain.domain.com is being sent to clientdomain.com

clientdomain.com wants to add a service that is usually run on a sub domain 3rdparty.clientdomain.com

how would this be done?
clientdomain.com domain control and just create a cname for a subdomain? is it that simple or does the multisite make that a mess?