My Super Heresy cabinets are only slightly deeper than stock & are based off of the Crites CS2 motor boards. as such, they're 21.25 tall x 15.5 wide x 15.5 deep, compared to standard Heresy/CS2, which are 13.5" deep. The passive radiator bass bins that I'm playing around with will give the cabinets the same displacement as a Forte, +/- 1%, which I believe is the same as your Tangent 4000, or at least very close.
I've basically followed Claude's instructions for his Super H build, then added tweaks here and there out of curiosity. I began with a pair of 1971 H700 decorators, which I first restored to Heresy 1 spec. Restored, I found them as unsatisfying as before and goaded on by Claude, I modded them bit by bit, so I could fully understand what each mod brought. First, I made new back panels (I didn't want to cut up my antiques) and added a 4"x4-1/2" B-52 port from Parts-Express. The port extended the bass response significantly, however, the Klipsch K-28-K woofers really weren't up to the task: the bass response was boomy and muddy- it was a step backward in SQ, even with significantly better low end response. Next, I replaced the woofers with Eminence Delta Pro 12A's: this really tightened up the bass response and improved the midrange, considerably. They sounded great! I left them like that for a few weeks, while I contemplated replacing the tweeters. My hearing has gotten damaged from many factors: growing up on a farm, playing in bands in my teens and twenties, US Army M110A-2 Howitzers, riding and ultimately racing motorcycles and roughly 30 years in construction has left my ears with a mass roll-off at 9750 Hz.
@Daveintn 's MAHL tweeters aren't cheap and I honestly didn't think they would make a significant difference, but ultimately, curiosity got the best of me and I ordered a pair. Holy cow! the sMAHLs made the single biggest difference in sound quality of any component in there. Somehow, they even made the bass frequencies clearer. these were hands down, the best sounding speakers I'd owned up until that point, although they weren't without deficiencies.
The 50+ year-old decorator cabinets were made with 5/8" birch plywood and they were "boxy" sounding to the extreme, even with foam and bracing, they had too much resonance. I also realized that I could probably flip the H700s and effectively get a new pair of Super Heresy's for free. I had a sheet of 3/4" Baltic Birch in my shop and I got to work building boxes. I ordered a pair of motor boards from Crites, as they were very reasonably priced and would save a lot of hassle with the router. I made the cabinets deeper, mainly to eliminate waste from cutting, although modeling suggested the additional 0.3 cubic feet would nominally increase low end response, I'm not entirely convinced it would be noticeable. I used K-701 & K-53 drivers because they were readily available and less expensive than the K-700/K55 combo and the rest of the parts were from the mods to the H700, although I made new networks with modifications to adapt the H-53 drivers, which were a little hotter than the K-55's. with stiffer, more robust cabinets, the Super Heresy were really, really good! I can't recommend them enough and I've encouraged quite a few people to build their own.
since then, I've been faffing about, chasing my curiosity. I picked up a single Klipsch K-361 pro speaker for a price too low to refuse, thinking I could easily flip it, only to learn why I got it so cheaply: nobody wants a single speaker. I parted it out, instead- the woofer alone covered the price I paid. I became curious about the mid horn and wondered if the bigger horn would improve the SQ, so I tried it. It did, with qualifications- the pro drivers with titanium drivers were not great, but I was encouraged enough to get another horn and try more drivers- I found a pair from PRV Audio that work quite well. Next, I wanted to tweak the crossovers to adapt the horns- the bigger horn could handle a lower x-over and driver overlap was significant;
@THD+N recommended a quasi- "universal" network that would address that, so with guidance from him and some inspiration from
@Deang I built one up. Significant improvement and I have the REW curves to demonstrate it! at this point, it dawned on me that my Super H clones were effectively chopped off Fortes, or not far from that and I began wondering if adding a bass bin with a passive radiator, similar to how many have gotten improved bass extension with bins on LaScalas, would improve low end response. A little math simulations showed that a 15-1/2" x 15-1/2" x 15-1/2" cabinet, added to the bottom of my Super H clones, would create the same internal volume as a Forte, within a percentage or two- while ports would be inexpensive (your Tangent 4000's) a 12" passive radiator would fit easily (Forte1) and 15" radiators could just be shoehorned in. I had settled on 12" passives when I found a pair of open box 15" radiators for roughly the same price, so I got them, knowing that I could also use them on a future project that I've been sketching out with assistance from
@ClaudeJ1 and
@Daveintn. (that will get its own thread when it happens). So I made a pair of extension cabinets with scraps from my woodshop. This weekend, I'll cut the bottoms out of my Super H clones and connect the two- it remains to be seen whether it would actually work, so I can't at this point, recommend the mods. I would go so far as to not recommend them until they've been tuned and measured.
If I were in your shoes, I'd simply replicate the Tangent 4000 boxes and put your Klipsch parts in them. Then, I'd replace the tweeters with L-MAHLs and perhaps replace the woofers with any of the drivers that have been successfully used in the Super Heresy Mods. While your tangents are a good third larger than Heresy's, as Claude's photo above demonstrates, they take up roughly the same amount of floor space and once could easily make the argument for WAF that there is little difference in the space they occupy, while there should be significant improvement in SQ. While Super Heresy are incredible, I'd imagine a Super Tangent 4K would be even more Super. You should do that.