Ask HN: Is it possible to send an SMS through a third party?

I've been playing around with Twilio and SMS for a few weeks now, and I'm wondering if it's possible to route texts through an intermediate party. Specifically, I'd like the end-destination reader to only see that the message came from the original sender.

Example of desired outcome: I send a text to Twilio with directions of who to send to. Twilio sends message out to recipient. Recipient only observes that I sent the message.

I have worked with DKIM authentification to handle this problem for email, but I don't think much of it carries over.