can a new amp amp tame my speakers?

I haven't actually heard the combination, in fact I'm not sure that the Kappa's I heard so long ago where the same as yours.
I do seem to remember that back in the day the Infinity IRS' (along with the Wilson Wamms) were the top of the line, most expensive speakers going. I could be wrong, but I think those IRS' might have used something like the emits that are on your Kappas. This is a long time ago, but I seem to remember that tubes were the only way to go with the IRS' (the bass panels had their own ss "servo" amps built in), and c-j tubes were a popular choice for them, but even with tube amps, some used to cover the IRS' tweeters with tissue paper to attenuate the brightness. In as much as that might seem to be an anathema on a speakers that cost around 50-60$K in the late 1980's, it was pretty effective. I even have a friend that uses the same fix today on some old Linn speakers.
Those IRS' midrange/tweeters did some magical things, and are still sought after today, but obviously they weren't perfect (at least IMHO).
I believe your speakers have a nominal impedance of about 6 Ohms, but I have no idea what the minimal impedance is. The use of self powered subs might be very advantageous with them, but that's purely speculative on my part.
As well as I can remember (not very well), I remember the Kappas as being OK, but found other alternatives preferable. You might very well disagree.
The c-j I hyperlinked is actually a tube/ss hybrid, seemed like a calculated safe choice. YMMV.

My Kappa's are way down the range from the IRS's, they are a 3-way box, and IIRC, retail was $1600/pr back then. The 8's and 9's were the real beasts, and many an amp went up in smoke, literally, trying to power them. I fully expected to be blown away by the improvements a $3-5K speaker could offer, but it hasn't proven true (yet). The PSB's sound wonderful, yes, but I'm struggling to hear $3-5K better. Plus I'm very aware that a better amp can bring more out of what I have, and the PSB's were on far better electronics than I have, so if the gap were to be closer when I upgrade the amp, it would be harder yet to justify a speaker upgrade. I had heard of the tissue-tweak as well, and wouldn't be opposed to it, but as I said, I'm mostly happy with the sound until I want to get loud. That's when things get ugly.

I appreciate all the input. Much has confirmed suspicions I already had, much has given me new directions to look, and with the consensus being that there's more to be brought out of the speakers I have, that's encouraging....

A good used class A krell amp,any model old or new class a/b would drive the hell out of your speakers with ease!,with very good sound!,you can find many used krells at different price points,depends on what you can afford,regardless,krell is known to drive any speaker! cheers!

Have you heard any other speakers besides the PSB's? Perhaps something like the Vandersteens 2's? The cost of which would be significantly lower, low enough to buy a really good matching amp too, for the same price as the PSB's. The used market has some steals too.

IF I change speakers, and it's a big if, I'd be more likely to have to get some that are more streamlined and 'fit' the room better aesthetically. The PSB's are 'approved' in that regard. Having said that, I've listened to B&W CM9's (I think that's the model, about $3K?), Paradigms in the same price range, Studio something's, neither of which impressed much, although a slight edge to the B&W. I did hear the 804's, and was impressed, but not in a particularly great listening setup. I heard the Vandersteen Treo (again, I think, about $6K) that someone was using to audition a TT. Associated electronics were also significantly upmarket on those, but they did sound pretty good!

I haven't covered all bases by any means, but so far what I've heard is leading me to believe that I'll need to get close to $6K to get to an improvement in sound that's more than just incremental and doesn't involve a compromise elsewhere - although I am also aware there would be a 'boost' to the sound of most of what I've heard by getting them into my room vs. the setups they've been in, but that applies to the PSB's as well. That I'm not ready for. I would be quite comfortable buying used speakers from that level though. I do see a set of Synchrony 2's on the 'gon for a great price, about 1/2 of list, and they are really tempting...
...but again, how good would they sound with the amp I have, a 25 year old Yamaha that was nothing special when I got it, never mind the march of time, although it's never missed a lick in all that time either...
What I'm looking at mostly is amps in the sub-$1500 range. I can't help thinking a good quality amp will bring the most out of the speakers I have, and when it is time to upgrade the speakers, I'll have quality to drive them with already.