A lot of call centres already serve more than one client. A prompt pops up on the agents screen for whatever company the caller is dialling and the screen switches to that companies system.
Ocassionally there is a pause for the agent but the call still comes through so thats why you sometimes get a basic "Good morning how can I help you" as opposed to Welcome to X". They are basically padding the conversation till their screen switches over
There is a certain amount of home call 'centre' work happening, mainly as it happens over VOIP. Its allowing people with kids etc to fit work around them. Its still a bit new and being watched for its potential but it will never become a major slice of the workforce as its too hard to control teh infrastructure in case of problems.