Thats the wrong order. You dont chose a dac/amp combo, and then look which headphone fits them. You find YOUR headphone, that suits YOU well. And then you get an dac/amp, that can drive them.
In my opinion: A 140€ DT 990 is NOT a good call for a 99$ + 99$ combo. 70-90% of the Soundquality comes from the headphones, and the dac/amp should not cost you more than your headphone.
That means, your Source (dac/amp) should cost about 30-70% of your Headphone price.
Even, if your budget is 400-450 bucks, then an 350-400€~ headphone (for example Beyerdynamic T90) on a 80€ Fiio E10 will perform better, than an 200-250€ DT 880/akg k7xx on the modi/magni combo. I guarantee it.
Alltogether, that will be 350 bucks, for 150bucks "soundquality". A Fiio E10 would fit MUCH better to the dt 990 Pro, because the cost-ratio from source to headphone is much better. And tbh, i doubt you will hear any difference there, except from the smallest nuance you could imagine. And even if... That difference will not be worth 120 bucks difference.
Another example: Dont buy overpriced dac/amp, get an Fiio E10k. That means, you are 100 bucks cheaper --> you can spend 100 bucks more for a better headphone. For example, upgrade the dt 990 to an Phillips fidelio X2. Brings you much much more, since the headphones are more important.
Some personal experience, to backup my argument: I used to have a pair of DT 880 edition with 600 Ohm, and got a Yulong u100 (should be comparable to the modi/magni combi~), while using my Asus Xonar DX (which is a simple 60€ soundcard without an headphone amp).
Tbh, i have heared almost ZERO difference at all. At best, there was like 1% difference in soundquality, if i was looking for it.
Believe me, the headphone is (in most cases. There are some headphones, that are known to need a lot of power. A Beyerdynamic is Not one of those, neither the Phillips Fidelios) MUCH more important for the soundquality, than a DAC or Amp.
Which means: If you pay 200 dollar for dac/amp, your headphone "should" cost at least 250-350 dollar.
As for the AKG K701: Great headphones, but they have a bit less subbass to be neutral (they are MISSING slightly bass at the botton to be neutral). But the resolution, clarity and soundstage are indeed superb.
Alternative: AKG K702 (check prices. Its the same with removeable cable), or AKG Q701 (the same, with just slightly more bass = not so "Boring").
Another one: Beyerdynamic DT 880. I have compared the dt 880 600 ohm with the akg k701, they sounded almost the same. Extremely similar. The AKG K701 had sliiiiiiiiiightly more resolution/soundstage, the DT 880 hat sliiightly more kickbass, which made him the better allrounder for me. Also, the materials are more tough/resilent.
Phillips Fidelio X2 is, in my opinion, pretty much a beyerdynamic DT 880 with a good bunch more bass (but still well controlled and punchy), that is NOT affecting mids/highs in a negative way. A lot basshead headphones have that problem, that they sound dull because of the bass. Didnt had the feeling here.
So, if you are not looking for a very neutral/balanced headphone, and want more fun, the Fidelio X2 would be my #1 choice there. Put the rest of your budget into an dac/amp, like the Fiio E10k, and be happy
