So technically you can do this now, but its a bit of a hidden feature at the moment 
It’s easy to do, however, we fear it could be abused, so it’s not as easy as pressing the inquire button is just yet.
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If you head over to your messages in the browser, you will see
https://www.morphmarket.com/messages/your-username -
Add a
/and the username of the person you wish to message.
https://www.morphmarket.com/messages/eaglereptiles/solarserpents will start a new message between us two for example.