Google and Office365 MX records on one DNS

I'm on Day #2 at my job here at the school district.

Scenerio.....

All students (5100) have only Google accounts...no problems

All staff have a Google account (lastname.firstname @[district].org)

and

Office 365 account (firstinitial+lastname@[district].org)

DNS has the MX record setup so that @[district].org goes to Google

BOTH 365 and Google emails use the same domain ([domain].org)

Can I setup my DNS to have 2 MX records pointing to Google and 365?

Is that a priority assignment setup?

My thinking is that when an email comes through that is the 365 address, the DNS will try to send it to Google first.  It will not find an address in Google. Then the DNS will go to the 2nd MX record and try sending it to 365.  Am I thinking correctly about messages and MX priorities?

Thanks!!!