Is my amp good enough?

I have had the NAD 375BEE for 8 years. Sweet sounding A/B Amp that comes alive with a tube preamp. Had a PrimaLuna 100 (6 tubes) but after trying a Rogue RP-1, I sold the PL. RP-1 can be had for around a grand. Upgrade the two tunes in the RP-1 and your current speakers will thank you for it. My experience in separates is that the preamp is what changes the sound the most (for the least amount of money) and that speakers are the most expensive upgrade and the least consequential. Surely, others will chime in that their Focals or Revel speakers made the biggest difference but at a major cost above and beyond what you currently have.

@neversatisfied 

The NAD 375BEE spits out 410 Watts into a 4 Ohm speaker. The Golds, at 4 Ohm, are rated at 250W RMS. (Think of 250W RMS as the average power your speakers will be given at any time). So together they are a good match with regard to specifications. 

Marrying up separates (varying manufacturers) can be daunting as making mistakes with your money can cause second thoughts and buyers remorse. But buying a set of new speakers that is highly rated is not really one of them. They are, after all, in the range of where you need to be in order to fill out your system with similar costing gear and they are highly rated with excellent feedback from other owners.

With relation to your intentions, your pre-amp, amp, source, and speakers should be in the 1K range with regards to price. If each speaker comes in around 1K each, that is a good fit for your overall plan of monetary attack. If you spend more on any one than the other - make it the source. A great DAC or Turntable will do more for your system sound (it's the starting point!) than any other component. 

It is reasonable that your current setup sounds a bit "thin". (I started my trek with the NAD 375BEE (with an NAD front end) and figure you are probably hearing what I heard many years ago). You likely only use a fraction of the watts of the amp (probably don't go past 10 o'clock on the volume dial in a listening session). So, a better set of speakers will push your amp to do more, which will end up creating "body" with regards to your sound. Think thick over thin. One surefire way to gauge this is to listen to your current speakers for a couple of hours and touch your amp afterwards. It will likely be warm. After installing your new speakers, and listening for the same amount of time, your amp will likely be much warmer to the touch - perhaps even hot - depending on the volume levels you are providing. This is proof that you have succeeded in making your gear work for you, or pushing it to the limits of what is is capable of doing. 

As others have said, another way to push your amp to do more for you would be to install sound dampening/baffles behind your speaker (and elsewhere) which again, allow you to be more aggressive with turning up the sound. Your amp should be working hard for you, but your speakers should be doing the same. Everyone here can agree that sound dampening enforces bass, which is another tool in the fight against a thin sound. Since you are forking out a couple grand, you should be asking the sales person to move the speakers you are buying around the showroom floor to understand how it works best in relation to your own room, as whatever dampening/distance from walls your speakers need in the store will be similar in regards to your own listening room.