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I'd treat your room before buying a new amp. REW is one of the greatest tools to get your room sounding its best and there are a lot of people to help you on the various A/V forums. You can even do DIY treatments (I have mix of DIY + some bought from GIK) and save yourself a lot of money.

Amplifiers, ESPECIALLY amplifiers made by the same company don't sound much different compared to the HUGE effect room acoustics has on the sound. In a receiver, the amplifiers are more limited in capabilities because of size, weight, and heat. But as long as your speakers are APPROPRIATE for the more limited capability amps in the receiver, there won't be any issues. How do you know if a speaker is a good choice to use with a receiver? The input impedance specification is part of the story. If the manufacturer says the speakers' impedance is lower than 6 Ohms, they really don't belong paired with a receiver. They need more current than receiver amplifiers. Some receiver manufacturers rate the power of their amplifiers using 6 ohm loads (resistors or speakers) because they get more watts into 6 ohms than they do into the speakers I recommend MOST for use with receivers... speakers with impedance specs of 8 ohms is perfect/ideal for receivers. Another spec important to note for speakers paired with a receiver is a spec called "efficiency" or "sensitivity". Those aren't EXACTLY the same thing, but they are so similar that I'm not going to make a distinction here... a typical spec for efficiency or sensitivity is 90 dB. This means with a microphone 1 meter from the speaker and 1 watt of power from the receiver, the speaker will produce 90 dB of sound (fairly loud, but not so loud that music would damage your hearing). If the efficiency or sensitivity spec for the speakers is 90 dB or higher... great choice for a receiver. 88 dB is OK if the impedance is 8 ohms or higher. Note that finding speakers with impedances higher than 8 ohms is unusual and the speakers themselves may work better with a vacuum tube amplifier rather than the solid-state amplifiers in most audio equipment. The thing about room acoustics is learning enough that you make POSITIVE changes and not changes that are WORSE than the untreated room. You will need software and a reference microphone (there are good reference mics in the $50-$100 price range, no need to spend more. Get a USB reference mic and download RoomEQWizard to your computer also known as REW. Run RoomEQWizard with your reference microphone and you can see all kinds of ways to display the data. There are online forums where people talk about using REW to help improve their own systems. One is on AVS Forum, but there may be others. Those forums are pretty near REQUIRED while you are learning REW since it's not exactly obvious what everything is for and when to use a frequency response curve versus a waterfall plot. As you learn more about REW, you should also read everything you can find about using room acoustics. The main thing about room acoustics is not doing TOO MUCH of any one type of room treatment. You have absorbent room treatments and reflective room treatments. Too much absorbing makes the room sound dead. Too much reflectance (from stone, glass, bare wood, etc.) is bad. In a glass room with stone, wood, or ceramic floring... there's already so much reflectance in the room you wouldn't want to add more of that so your room treatment should focus on absorptive devices. If your room is full of large overstuffed furniture with fabric coverings, heavy curtains, quilts or rugs on the wall for decor, etc.... you may want no more absorptive treatments, so you would focus on reflectance devices. This is a complex aspect of the high-end audio experience... I found it massively useful to learn since I've moved enough times that I've had to "start over" with a new room 8 times since I got into high-end audio. Each time I learned more about room acoustics. Even if you don't move, you may learn things that can improve things enough to make them worthwhile. So never consider your adventures with Room Acoustics to be over. You can ALWAYS improve the room. Anthem has their own room acoustics processing in their receivers. If you have not learned how to use that, it is a good place to start.

The amplifiers in Anthem's receivers are considerably better than the amplifiers in Asian receivers. And the Anthem receivers can drive speakers better than Asian receivers. If you do ever get to the point where you get a new amplifier, consider just a stereo amp. Put the main speakers on that amp, and all the other speakers on the receiver. Or use a 3 channel amp and put the main and center speakers on that amp and everything else on the receiver.

The answer to the “what to fix” question depends on what’s broken.

Most of the time, amplifiers are pretty darn good. Most of the time, untreated rooms are just OK, although that is the great variable. So I agree that, most of the time, room treatments will be more noticeable than a 25% increase in amplifier power. But figuring out what’s broken is an important first step.

If your goal is to correct any acoustic anomalies in your listening space, treating the room is undoubtedly the way to go. But unless you have a good knowledge of acoustics, this is not a DIY process. The REW software is not difficult to learn, but interpreting the results and correcting them is not a job for a novice. A friend of mind bought the REW program and a recommended microphone. I was going to borrow it, but after watching him try to figure out his results, changed my mind. Your experience may be different.
There are plenty of articles on S&V describing ways to avoid compromising audio quality. One thing to consider. While it likely won't improve the sound, it's a hell of lot more exciting adding a new amplifier to your system than hanging a bass trap on your wall.