Relaying disallowed (I know why, but need to know if still possible)

Relaying disallowed (I know why, but need to know if still possible)

So, my Magento site is a multivendor marketplace. I allow vendors to invite sub-vendors through a customized module, where they enter emails and a short text. The template is a site template that auto-inserts their short text into the template when sent. The email shows as sent by the vendor's email. However, after switching to Zoho, the emails are no longer sent and I get 

ERR (3): 
exception 'Zend_Mail_Protocol_Exception' with message 'Relaying disallowed as Username < xxxxx@email.domain>
' in /var/www/mydomain.net/lib/Zend/Mail/Protocol/Abstract.php:431

(Except < xxxxx@email.domain> is the sender's email)

I understand that it's disallowing it because it's not the email I use to send other messages/emails from the site. Is it possible to allow this to work though?  Or is my only option to make it so the emails are sent from my account's sender email?