Is it possible to set two MX records for one domain?

Solution 1:

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.

Solution 2:

Dual MX records are used for backup purposes, i.e. if you list more than 1 MX record for a domain, any host attempting to deliver email for that domain will only attempt such delivery to 1 MX at a time.

In order to achieve a dual delivery as described in your question you will need an SMTP service that receives email for your domain/s, and that SMTP service would perform delivery to multiple endpoints, e.g. for each message it delivers once to Google Apps and once to Live mail.

This is not common and almost certainly not a good idea, maybe you can clarify what it is you are trying to achieve?