Sendgrid supports this and we have used it to allow our users to have our system send emails on their behalf. The caveats are: (1) your email will contain info

Sendgrid supports this and we have used it to allow our users to have our system send emails on their behalf. The caveats are: (1) your email will contain info in the header that indicates it's on behalf of, which probably affects deliverability somewhat (we got very good results nonetheless) and (2) to get good deliverability your account probably needs to be at least "silver" level service which gives you dedicated IP address and some associated whitelabeling DNS entries. In other words, the more trustwoorthy your mailer domain is, the better deliverability you will experience.