What it was given
- System
- Sennheiser HD 650, Schiit Modi 3 and Magni 3
- Room
- Headphones only, open plan office
- Budget
- $400
- What they wanted fixed
- it sounds flat and closed in, I want more space and air
The short answer
Change the headphone, not the electronics. The HD 650 is a warm, intimate, closed-in-staging headphone by design, and no amp or DAC will turn it into a wide, airy one. Put the $400 into a HiFiMan Edition XS and keep the 650 for the nights you want that thick, comfortable sound.
Why this and not something else
Your weakest link for the thing you are asking about is the transducer, full stop. "Flat and closed in" is the HD 650's signature: gently rolled treble, modest air, a stage that sits between your ears rather than around them. People spend years chasing that out of it with amps and never get there.
Specifically, I am not recommending an amp upgrade. The Magni 3 has plenty of voltage swing for 300 ohms and is already transparent; moving to a Burson or a Woo would change the tonal flavor slightly and would not widen the stage. I am also not recommending a DAC step to a Qutest or Ares II. At $400 that money would buy you a difference you would strain to hear on a headphone that is the limiting factor.
One thing to be honest about: an open plan office has a noise floor, and low-level air and decay are the first casualties. Some of what you are calling "closed in" is the room eating the top two octaves of ambience. A quieter listening spot will do more for perceived space than any $400 purchase.
Now
HiFiMan Edition XS, roughly $400 to $500 depending on sales; it is discounted often, so wait for one. It is efficient enough that the Magni 3 will drive it properly, and it is the cheapest genuinely open, airy, large-staged headphone I would put in front of an HD 650 owner. Buy from somewhere with a return window: HiFiMan build and headband comfort are the real risk, not the sound.
Next
Nothing for at least six months. If, after living with the XS, you find it thin or a touch splashy on cymbals, that is the moment a warmer source starts to matter, and a Modi Multibit or Ares II would be the move, not an amp. That is a $200 to $800 decision to make later, with a specific complaint in hand.
Where it ends
For headphone listening, diminishing returns start hard right about here. HD 650 plus Edition XS covers warm-intimate and open-airy, and a clean transparent Modi/Magni stack does not hold either of them back in a room with a noise floor. A sensible stopping point is exactly this: two complementary headphones, one honest stack, and no third step. If you ever get a quiet dedicated room, revisit it then; until that changes, spend the money on records.