Currently onMessage only supports Google Analytics, which doesn't allow tracking users across various sites.  Adding Google Tag Manager to onMessage should be very easy as you just need to insert Google provided code to both the HEAD section of all pages (can do this already with the current Google Analytics SEO part) and the BODY section (this is currently not available in onMessage).   Adding support should only require the addition of another box within the settings to put the Google provided code in and then make that appear right below the BODY tag on all pages.

Having Google Analytics enabled is very important in this time and age so that we can track a visitors entire journey from perhaps social media discovery of the school, to our website (onMessage) to application (onBoard).