I've got some modified DT-770s, I'd definitely pair it with an amp... Granted your source is good. No use in amplifying a poor source. Mine are running Modi Multibit > Vali 2 with a Gold Lion tube, they sound wonderful. I'd like to try a SS amp though. It has been a while since they were fed through one, but I remember it being nice. You can't go wrong with the Magni 2. Someone on the forums here was selling an Asgard 2 for like 140 USD, crazy deal. Might wanna dig through there and find if it's still available.
Also, the Alpha Pads on the DT-770 is a crazy good pairing. They're expensive af, but they're really, really great.