I've got this friend who's looking for well-designed cat furniture  

Cool pet furniture
Sure, it's out there, but it's way overpriced... like most things pet-related.

The answer is in your question
".. even if I have to build it myself."
You can make your cat and yourself both happy by making your own modernist cat tower. My cat (who we lost last January after over 17 years) flatly refused to spend time with any kind of store-bought bed or play thing. She seemed to prefer hanging out on our best modern furniture (or laying on me).
Just considering the possibilities makes me wish I'd tried fabricating something modern and feline-friendly for our cat. Right now I'm thinking of an all white Bauhaus-inspired construction, or an Eames-ish jungle-gym made of off-the-shelf materials. I think with a bit of inspiration and rudimentary skills one could put together something pretty cool that would not clash with your high design interior.

You could start
with something like the Rietveld chairs in this thread, and build from there ?
http://www.designaddict.com/design_addict/forums/index.cfm/fuseaction/th...

Speaking of Rietveld, take a...
Speaking of Rietveld, take a peak at the newest Modernism magazine ad section in the back. You should see a dog house. I believe there's also an ad for wall mounted ellipses for cats. I say believe because, sigh, I've lost my copy.

The Ekstrem chair (from Rietveld thread) actually would serve handily.
If only it was available in sisal.

There's this on Etsy -- it's like...
There's this on Etsy -- it's like the feline version of "unhappy hipsters"!

Maybe you could make somethin...
Maybe you could make something de stijl ish out of scraps of pine?
Or as like the last one take a small sheet of ply and screw a heap of scraps (wider boards for platforms) on from the backside and then attach that to a wall.
Havn't had a kitteh since I was a kid so not sure if it would appeal.

How about an indoor "zen garden"?
They'd love it!
http://www.oberwelt.de/images/bis2003/20000428_michael_goering/zen%20gar...

WHC
And so it begins. You start with just the sisal post...then think "what could it hurt to get one a teensy bit bigger"
next think you know you're that crazy cat lady that the parents tell their kids to avoid during Trick or Treating.
😉
Of the three little beasts I've lived with in adult life I found one preferred being up high and/or being inside a box. One preferred a hammock by the window. And one preferred clawing the hell out of my couch.
I really like the idea of the modernist cat tower encompassing several elements: scratching post, height, enclosure.

There are some very decent modern cat furniture things out there.
moderncat.net is a blog site that has links to all kinds of stuff, both pricey and reasonable.
I should think you might allow your kitty to enjoy some of this swanky kitty stuff! We have the kitty condo shownb below from moderncatdesigns.com which we found through the moderncat.net site. We, and by that 'we' I mean myself and my four-legged children, also highly endorse the 'catclaws' scratching posts. They're made from layers of corrugated carboard and are fun to sleep on as well as scratch...well for them it is. You can find them through the same site.
http://www.moderncat.net/

Heath's
last image above makes me think of Louise Nevelson sculpture -- and of a "cat climbing wall" of, maybe, carpeted blocks and slabs ?
You'd never know if your cat would use it or ignore it, until it was done -- so better make it with the idea of an art piece -- and hope for the best !

This "Hollywood Franklin Cat Tower" thingy is pretty impressive--
You take an Ikea Stolmen-system pole & mounting hardware, then you can buy these platforms (in your choice of Flor carpet colors) to build a tree. Not exactly the "gymnasium" I have in mind, but still an impressive Ikea-hack idea.
http://www.etsy.com/listing/73355480/hollywood-franklin-tower-modular-cat

I like the look of that too...
but the domestic destruction that will be wrought by frisky felines launching themselves from that thing is more than my poor heart can bear.

Something like those hidden b...
Something like those hidden bracket ikea shelves running up the wall with carpet tiles stuck on them (I think there is low voc waterbased adhesive for that now) might look good, almost like the floating steps in Mr Odas' house posted a few days ago.