Is there a remedy?

+1 on Cabinet/driver/wire are the most likely culprits

I had internal wire buzz in martin logans in both speakers. The wires will buzz either against the driver, cabinet or the crossover components. Fixed it with self adhesive weather tape in the places where wire was close to other components.

Maybe start off by tightening the driver fasteners first? The do get a bit loose over time. 

Treynolds155 gives excellent advice. I just sent a text to an audio buddy of mine last night suggesting that he tighten the driver fasteners on his speakers. You wouldn't think they would be loose in the first place and you wouldn't think it would make that big of a difference in the sound and you would be wrong on both counts. It's a good place to start and at the very least you will get a much tighter and more focused sound if they are even slightly loose

If tightening the drivers doesn't work you will need to find the source of the buzzing. As mentioned above, it might even be something other than the speakers. The problem is that it only occurs when playing very loud. You can't be holding your ear next to a driver while it is producing 120 dB at close range. My recommendation is to buy a pair of Etymotic Research ER20 earplugs available on Amazon (and elsewhere). They are designed to reduce the sound level more uniformly across the frequency spectrum.

If you or anyone you know ever attends live amplified music shows these earplugs are absolutely wonderful. You can hear everything while saving your hearing. They also make great stocking stuffers!

When I had my recording studio I bought them in quantity directly from Etymotic. I gave them to the members of the bands I recorded (I did a lot of metal and hardcore) along with a lecture about preserving their hearing. The Etymotic guy asked what I was doing with them and when I told him he gave me an extra discount. Great people.