This is an interesting little amp. In general my advice is to upgrade headphone first, then follow with amp later. But looking more closely at the SMSL AD18 I might propose putting a little bit of budget first into a DAC/AMP that is more focused on headphones than speakers. This device is definitely more of a speaker first product. The headphone out put is 53mW into 32Ohm. This is on the lower end for most headphones you are looking to upgrade into. They may get loud, but without a little more power you won’t get the performance you hope for. Headphone impedance will vary over frequency, and in the lower frequency range having more power will give the amp better control over the driver. Everything will tighten up with a better amp.
My 2 cents: get a schiit magni/modi stack, or an atom DAC/amp stack, or something similar. Even a DAC/Amp combo like a Schiit Fulla, or Fiio K5 pro will do the job. Even your current dt770 will sound better on these. And then you’ll be in good shape to get Sundara, HD6xx, or whatever you want to try next. Tons of great next step options.
Also worth thinking about is the used market. On this forum you can get entry level DAC/Amp for a good price, which will leave some $$$ for the headphone purchase.
On the headphone side, either the Sennheiser HD6xx or HD58x are interesting next steps. The Sennheiser sound on these is definitely different than the dt770, more neutral (not really a neutral headphone, but more that way than dt770). Getting the HD6xx is an interesting option because so many people have it, it is often used as a reference in their reviews.
Sundara are a great introduction to the planar magnetic sound with an overall neutral sound and good bass extension (not elevated bass, but quality bass).
Going a completely different direction, but interesting to get a better sense of what sound you like, you can try the Grado SR60 or SR80. SR80 have a slightly more elevated bass region, which may fit your taste coming from the dt770s.
If you want some cheep thrills, try the koss kph30i ($30 on Amazon). They will sound great on your current amp, and will blow your mind when you upgrade. $$$ per unit fun, these can’t be beat. I pull these out from time to time and question when I’ve spent so much on other cans.