Send emails with different FROM and MAILED-BY (MAIL FROM) addresses

I have my domain setup in SES with a subdomain for a custom MAIL FROM address (works all fine, I can send from it), lets call it mail.foo.com, but I am restricted to setting the 'from' address as emails under that domain (myEmail@foo.com). However I have somewhat unique circumstances where I am sending emails on behalf of clients and I want the message to appear as if it came from them (say theirEmail@bar.com) but still keep my domain, mail.foo.com, (which has SPF, DKIM setup) as the the MAIL-FROM (shows up as 'mailed-by' in gmail). Adding their emails as verified emails is not a problem, but if I send from one of those emails the mailed-by address is amazonses.com, and as I said before I would like that to be my mail.foo.com.

To summarize and rephrase, I want to be able to do from: 'sender name theirEmail@bar.com' mailed-by: ''mail.foo.com" (which i own and have setup)

But right now i can only do

from: 'sender name theirEmail@bar.com' mailed-by: ''amazonses.com"

or

from: 'sender name email@foo.com' mailed-by: ''mail.foo.com"