My view of the hierarchy of a audio system is: Speakers, amp, DAC, streamer. (ok, I'm waiting for the counter comments already)
My journey and experience are different, and I wish to offer an alternative perspective—not a counter one. I believe both ends of the chain, and every piece of gear in between, are equally important. You want the full potential of each component to be explored, leaving no weak link. I invested in and auditioned my amp and speakers around the same time, about 2–3 years ago, and since then I have never felt the need to upgrade them. However, I do rotate them between two rigs, which lets me enjoy a fresh sound every now and then, especially when I upgrade my digital front end and cables, including streamer and DAC. At this point, I’d say I’ve finally explored the potential of my amp and speakers—or at least come very close.
“Garbage in, garbage out.” It’s a simple phrase that captures the essence of any production or reproduction system. In audio, however, the reproduction chain between the “in” and “out” must be capable of preserving the quality of what is fed into it. In your case, if I were you, I would eliminate the weak link in the chain first and then evaluate the system’s performance over a full burn-in cycle before embarking on upgrading components that are already top-notch.
If you’re craving a different sonic character, that’s a different story. But even then, it’s always wise to proceed sequentially—one step at a time.