I've listened to many Magnepan models over the years but never heard the model IIIs. As I understand it, one of their best features is the true ribbon treble section and one of their worst is being about 25 years old. But I believe you having them recently fully rebuilt, including the ribbon tweeter, probably extended their lifespan for another 25 years.
I recently bought a pre-owned pair of 3.7i, upgrading from a pair of 2.7QR that were also about 25 years old. My decision was much easier, though, because the 2.7QRs have the quasi-ribbon treble section and I wasn't considering having them rebuilt. I've powered both with a pair of D-Sonic M3-600-M mono-block class D amps rated at 1,200 watts at 4 ohms with very good results.
I noticed a significant improvement in the treble performance and detail levels with the 3.7is that you're probably already experiencing with the IIIs. I believe all 3 models, the 2.7, 3.7i and III, have similarly sized quasi-ribbon midrange and bass sections that are very good but only have bass extension down to about 35 Hz and lack the capacity of powerful bass impact and dynamics.
However, I also understand the symptoms of upgrade fever very well. My suggestion is that you keep your IIIs and satisfy your upgrade urgings by buying a high quality bass system like the Audio Kinesis Swarm complete bass kit for about $3K reviewed here:https://www.theabsolutesound.com/articles/audiokinesis-swarm-subwoofer-system/
I've been using the very similar and equally priced Audio Kinesis Debra complete bass kit for over 4 years now and it's the best upgrade I've ever made to my system. I can confirm that the above review gives a very accurate description of what bass performance levels to expect.
These bass systems are based on the scientifically proven effectiveness of the 4-sub distributed bass array (DBA) concept developed by acoustic expert Dr. Earl Geddes.
Prepare to be amazed how extremely well the 4-sub DBA system will work with your Magnepan IIIs. You would continue to operate your IIIs full-range and either the AK Swarm or Debra complete 4-sub DBA system will extend your system's bass down to 20 Hz +/- 3dB and the bass will be powerful, dynamic, detailed, smooth, fast and natural in virtually any room and integrate seamlessly with virtually any pair of main speakers. So, , it would likely be the last sub system you'll ever need to buy, even if you move or choose to use different main speakers.