“Complex” can mean (1) complicated, (2) a psychological fixation, and (3) a group of buildings. One can have a “complex complex complex.” The “complex” pun has been cited in print since at least 1969.
 
“What do you call a dying airport computer?”/“A terminal terminal terminal” is a similar joke.
 
     
11 August 1969, Chicago (IL) Tribune, editorial sec., sec. 1, pg. 24, col. 2: 
COMPLEX
A cluster of buildings is called a complex.
 
A psychological fixation is likewise called a complex. Thus an architect who insisted on designing nothing but industrial complexes would have a complex complex.
 
Complex is also a word meaning complicated. If the architect’s personality were complicated by other factors as well, he would have a complex complex complex.
 
21 March 1997, Pittsburgh (PA) Post-Gazette, “Grammar Lady” by Mary Newton Bruder, pg. C-24, cols. 2-3:
TRIPLE PUN OF THE WEEK: As far as triple puns go, I must tell you that at one time I had a “complicated obsession with interconnecting buildings.” You guessed it—I had a complex complex complex!!!
     
Google Groups: alt.usage.english
3 words in a row was: Obfuscations and anomalies
John Packer
11/10/98
There was an engineer who enjoyed producing drawings of complicated structures so much that he started seeing a theripist. You could say he had a complex complex complex.
           
Google Groups: alt.callahans
RECYCLED HUMOR: Bad Jokes I Found in a Fine Clothing Catalog
deidre carpenter
12/1/00
(...)
> If you have a psychological quirk about complicated apartment houses,
> could it be said that you have a complex complex complex?
>
> Miche
 
Hooo-weee!  Nothin’ simple about *that* psychological quirk!.... so it must be a pretty complex complex complex complex ....
 
Google Groups: alt.religion.scientology
Collecting up Scarff Hate posts re Gerry Armstrong
Shy David
10/29/02
(...)
“That reminds me of the psychotic architect fixated on intricate industrial parks; he had a complex complex complex.”—- Marty Leipzig
 
Twitter
Daniel
@danw
Replying to @alainp
@alainp reminds me of the architect who had an unhealthy obsession with large, intricate shopping malls. He had a complex complex complex.
4:03 AM - 20 Oct 2008
   
Twitter
Jed Batchelor
@djjeddyb
Just thinkin, if I had a complicated fear of indoor shopping centres….could I have a Complex Complex Complex ??? Hmmmm
12:00 PM - 20 May 2009
   
Twitter
Starski111
@starski111
I’m scared of places like shopping centres particularly if they are confusing & difficult to navigate. I have a complex complex complex.
4:29 AM - 25 Sep 2011
   
Twitter
Madhattin’ Project
@PurePlatonium
Once met a guy who had an irrational fear of overly intricate clusters of commercial buildings. He had a complex complex complex.
9:30 PM - 18 Apr 2012
   
Twitter
Gordon Holbein
@strategicGFH
If you have an intricate psychological obsession with large industrial facilities, you would have a complex complex complex.
11:48 PM - 24 Nov 2012
   
Twitter
Miriam
@GamesABogie
I have a phobia about complicated large buildings, doc says I have a complex complex complex.
7:04 PM - 26 Jun 2013
 
Reddit—WordAvalanches
I suffer from complicated anxiety about an elaborate group of buildings. It’s a complex complex complex complex. (self.WordAvalanches)
submitted February 22, 2014 by dan1point5
           
Reddit—Chemistry
I have an irrational fear of going into our inorganic chemistry building. (self.chemistry)
submitted March 13, 2015 by mlukemanPhysOrg
I have a complex complex complex complex.
   
Reddit—Jokes
I have an irrational fear of large intricate corporate buildings.
submitted May 20, 2015 by Reziarfg
You could say I have a complex complex complex.
 
Reddit—Jokes
I have a phobia of over engineered buildings
submitted November 20, 2015 by Krabo
It’s a complex complex complex.
COMMENTS
SaddleDaddy
That’s why I live in a house, because I have an apartment complex.
 
Reddit—Jokes
I have a phobia of over engineered buildings…
submitted June 3, 2016 by buymeapickle
It’s a complex complex complex.
   
Reddit—Jokes
I have a phobia of over-engineered buildings.
submitted September 9, 2017 by PatrickChase
It’s a complex complex complex.
 
iNews (UK)
100 pun-based jokes that will make you laugh and cringe
by Alex Nelson Friday June 29th 2018
(...)
I’ve got a phobia of over-engineered buildings. It’s a complex complex complex.