Less is more? Where's the midrange question -help

I've been furiously wondering about this for years -
Be kind, I'm just now making the move to serious audio!

In short:
Why is it that when you move past Polk, Mirage, Klipsh, whatever upper low end, and move onto mid high end you lose the implied technology and number of drivers? Most of the lower end stuff at Tweeter or Circuit City (sorry) have a tweeter (or horn), a midrange or two, and a woofer. Moving up the scale and dollars results in speakers with only 2 drivers.... How do you get accurate midrange from a 4" or 6" driver?

To be more specific -
I have recently purchased a pair of Audio Physics Tempo III's. I have yet to find the sweet spot. They sound muddled and harsh. I have a Yamaha amp, but will be upgrading shortly to an Aragon 8008 ST.
I am listening in a somewhat small room, plan on moving the equipment into the basement shortly.

Here's the reason for the question and thanks for reading this far down!

I have two (be kind) Radio Shack Super Tweeters that I think sound incredible. They were $20.00 each 10 years ago. They seem to bring definition when hooked up in parallel with my Tempo III's... more to the point, I have Klipsch satellite speakers (in plastic boxes about 6" high) which bring out the midrange and clarity of strung instruments when hooked up in parallel or simply playing as "B" speakers while the "A" speakers (Tempo III's) are playing.

How do you get the midrange with out a driver tailored for that frequency? Do my $3,400 Audio Physics Tempo III's have a midrange deficit?

Any revelations for ideas greatly appreciated!!!
Are your speakers new? If so, plan on playing music through them continuously and pretty loud for about 100 hours before they'll reach their real sound. The driver's surrounds really need to be flexed quite a bit to work as designed. The "harsh and muddled" description sounds like a not yet broken in speaker.
I would suggest more than 100 hours is required. More like 200 before they sound 'right' (open, airy, etc.). And then will continue to smooth out for another couple of hundred hours. Nothing makes them sound better than playing them. They need the work.
Sounds like you would be happier with other speakers. What else did you audition before you purchased. I would recommend Tannoy D500, Thiel CS2.3/2.4, Energy C9. Any of these speakers will have a more forward midrange. They should all be easy to find used for reasonable prices.

However, looking at your amplification. You have to take care of it. It is probably a big part of the reason you are not satisfied with your speakers. I would recommend a used Sim Audio W-5. It has nice top-end extension with enough power to drive any speaker you are likely to purchase. Any other 200+wpc SS amp should do nicely.
Good drivers with uniform frequency response and low distortion are not cheap. Good passive components are not cheap. By the time everyone gets their markup the sticker price can be 10X what the components cost. Ergo for some definition of "affordable" and "high-end" affordable high-end speakers are 2-ways.

Good (expensive) drivers are also often useable over a much wider frequency range - tweeters with low resonant frequencies can be crossed over lower, mid/bass drivers with low inductance and phase plugs work well higher.

The best midrange I've heard from a dynamic driver is with an 8" Seas Excel in a 3-way configuration. It's at least in the same league as ESL midrange, although I haven't listened to that recently enough to pass judgement.

However, bass _will_ cause midrange IM and doppler distortion in 2-way designs, especially with smaller mid-bass drivers. A sub-woofer with an 80Hz high-pass (preferably 4th order) works _wonders_ to fix that.

You might look at your source.

If by Yamaha amp you mean a receiver, it may have problems with the 4 Ohm loads at high levels.

You may just not (yet) like your speakers.

Break-in is mostly listener break-in, even on speakers. You will get used to the sound and not notice inaccuracies until you compare it against a live performance. Different sounding speakers will sound wrong in comparison. Similarly, your old (broken-in) speakers will sound wrong if they're sufficiently different from new speakers you've lived with for a few months.
I heard those speakers and a few other AP models. I bet you didn't hear them before you bought them! AP's have a very specific sound. I believe a really deep soundstage is what they all have in common. Without proper placement and lots of system matching you are just going to get a recessed midrange and a muddled sound. I don't think the goal of the designer is going to be met by adding additional speakers or supertweeters. As far as my opinion- i don't like them. I prefer a more intimate sound. Nice full mids. Despite that (!) I own the VirgoII. I think they are the best of the bunch- but- I spent a lot of money on electronics to get them to sound to my liking (and they sit in the middle of my room).
You should love the sound for $3500 even if your electronics are not the best. Get rid of them. Buy some Vandersteen's and keep the change. Just want to add- I read the Stereophile review on the new VirgoIII. Velvet sound? I did not hear what he did.