So, I have some Grado SR60i's that I got to dip my toe in audiophile sound, and I'm really happy with them. But, I've been itching to get something else to expand my understanding of sound. I know I will pick up some of the lower end Koss items, because of what I've read and because I live right by their headquarters. But, I have a few questions:
 
1. Should I invest in a DAC, or another pair of headphones?
2. What DAC would complement the Grado sound signature?
3. If I were to get another pair of cans, what set of headphones sounds completely different to Grado? 

What amp/DAC are you currently using? If you're using something like a laptop, you might get some improvements from a USB amp/DAC, but it won't be very large unless you're currently getting audible noise, hissing, popping, etc. You might need one for a different pair of headphones, though, just to get them to a reasonable volume. In general, unless you need more volume, your money is better spent on headphones.
 
I recommend you don't compliment a headphone's sound signature with more colored gear. You can do this much more accurately with a digital equalizer, and for free! If you really like a piece of gear, get it. That's just part of the hobby. But get it for the right reasons. Not because someone tells you it'll transform your SR60i into a whole new headphone (hint: it won't). Differences between amps and DACs are grossly exaggerated anyway; most are dead neutral, some are badly rolled off or distorted.
 
As for sound signature, check out dark, bassier headphones. I can't promise you you'll like it, because I don't know your tastes or what you listen to, but it'll definitely be different. The Koss PortaPro would fit the bill well enough, for the price.
 
You can also go for something with a large soundstage, like a Q701. It's kinda hard to make recommendations without knowing your budget BTW.
 
Ask Koss if they'll let you demo the ESP-950, their flagship electrostatic headphone   

Oh, yeah! Those things would help a lot, wouldn't it? 
 
So, I listen to a lot of rock music, mostly on the experimental side of it. I estimate 85% of my music tends to fall under the umbrella of rock, even if it's hard to tell what subgenre it is. The other 15% is a mix of most other genres (The exception being country.)
 
I'd like to keep this next purchase under 200 dollars, and it's even better if I could fall way short of that amount. 
 
And the general advice is to get a DAC/amp if your sound card is bad, or if your headphones have a really high impedance? But that will marginally improve the sound quality if you use it with low impedance headphones? Good to know!

Bump?

So, I've narrowed it down a bit. I decided I wanted something that's both practically different and sonically different. So, most of these are closed back and over ear. Still taking suggestions, though.

-Audio Technica ATH-M50x
-Sennheiser Momentum (both on ear and over ear versions.)
-Berdynamic Custom One Pro.
-Sennheiser Urbanite (Both versions.)
-Sennheiser HD558 (The exception.)
-Beats Solo 2 (I've heard they're pretty good?!? Why not at least try them out?)

Hopefully I'll get the chance to test these out at a Best Buy or Apple store...