That's exactly what I was referring to. My attention is drawn to those boosted levels, and away from the song I was listening to. That's bad.
An amp would help if the Marantz cannot provide enough clean power to achieve your desired listening levels.
Remember, amps just amplify, they're not tone controls. That's the case for the onboard amps in your Marantz and any other power amp you've mentioned.
Now, with your appreciation of 'loud' and that your 703 S2 may have the challenging load typical of B&W speakers, I wouldn't rule out more powerful amplification, but let's not jump the gun. You're still in the "optimize what you already own" stage, not the "shell out more ducats in an under-informed, consumerism-driven shot in the dark, hoping it will cure my sonic ills" stage. It is prudent to thoroughly assess the problem before implementing costly, potentially unnecessary solutions.
You should try one of the online peak spl calculators to get an estimate of your actual power needs. Your Marantz is reasonably capable in terms of power, possibly more than adequate for your needs.
Don't believe the hype. You should forget all you may have heard about Marantz sounding "warmer", "more musical" etc.