Amp's that are better sounding than a nad 3020

You would be amazed what $300.00 can buy. TheYamaha R-N303 has a formidable feature set and a very decent amplifier and if you can find one it sells for $329.99. Then there’s always the yard sale treasure possibility. 

It's like asking, "what's faster than a Geo Metro?"

Just stick with the NAD - it is perfect in that budget.

Find a reasonable Exposure integrated amp. Save and spend a little more. You won't regret it.

As like @ozzy62 said:

I doubt you are going to find anything that sounds better than the NAD for 300.00. Save your pennies, then move up...

Unless there is a problem you’re trying to address, then what is the point of “moving up”?

I would think a sub woofer, or a source, or some room treatment or a slab of beer would likely bring more joy… than moving from a good $300 amp you own, to another good $300 amp you need to find.

What it is not doing that you more of?

These are always hard decision, but knowing the goals and requirements is always time well spent to get clearly into the thought process. (IMO)