While you can set up more than one MX server for a given domain, this is purely a backup function to specify another server to receive mail when one server goes down. It’s not possible to let two totally different services both handle your mail for the same domain, and IMHO it doesn’t make any sense to even try. If you like Google’s features better, switch to Google, otherwise you have to live with what Live Mail offers.
What might work is to forward mail from Live Mail to another domain hosted by Google, but then you would need to manage two separate services.