Is it possible to have two different email services handle emails for a single domain?
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.
At this time, it is not possible to let two totally different services both handle your mail for the same domain, as the emails are sent to each server depending on what the priority of the MX record is, from 0 being the highest priority and the priority getting lower as the priority number goes up.
Gmail is a good example of how multiple mx records will work. Multiple servers have lower priority, so if the primary server cannot receive the emails, the email is handled by the next server by priority in the list. Below will be the mx records for Gmail as an example of multiple MX records from their knowledge base here.
@ or leave blank
|@ or leave blank||3600||MX||5||ALT1.ASPMX.L.GOOGLE.COM|
|@ or leave blank||3600||MX||5||ALT2.ASPMX.L.GOOGLE.COM|
|@ or leave blank||3600||MX||10||ALT3.ASPMX.L.GOOGLE.COM|
|@ or leave blank||3600||MX||10||ALT4.ASPMX.L.GOOGLE.COM|