The box that was mentioned is the AX-20 mixdown panel which Teac made when folks back then did not
have a mixer yet, to try and make the mixdown process a bit more simplified.
Anyhow, its good to go back to the original post and re-read what his intentions are with his A-3340. To me, it sounds like he just wants to enjoy it as a hobby (same with me). Its not like there a band with a drummer that would need a whole bunch of mics going into a console and so forth. For just one guy by himself, wanting to do some basic recording/overdubs, the mixer does not have to be too complicated whereby you get dizzy just looking at it and trying to find where the modern-day tiny bargraph meters are on it- vs the ergonomics of a 2A/MB-20 that match nicely with the 3340, as it was meant for- everything is very clear from the VU meters to the 4 assign pushbuttons across 6 channels.
I just suggested, being he has a vintage A-3340, that when he considers mixers- he can start by considering which one was originally the best match- thus 2A/MB-20. If he finds it not to his liking, then he can move ahead chronologically to 80's and 90's Teac/Tascam products- as I mentioned previously, I have an M-30 and M-1516, and despite those, it did not compel to throw my 2A/MB-20 away in the trash as if it worthless. But for his needs, I dont think an M-30 is necessary unless he plans to make more elaborate recordings, and ditto the M-1516 which can be more useful with 8 track machines- I find it to be a good unit, have not had any issues, and if anything, I appreciate it lighter-weight construction, at age 61 and getting older, I dont want to risk a hernia trying to lift and carry it anywhere if I had to move it somewhere else.
Its not clear where he would be looking to buy a mixer, if its a vintage one, then I presume Ebay, in which case, its always good to get some background history and details from a seller, and hopefully buy one that was fairly well maintained (as my M-30 was).
One more thing to clarify on the 2A- there are usually no shortage of them on Ebay, and though prices for most things are higher than they were some years ago, a 2A wont burn a hole in the wallet to be a risky buy, but its really good to have the MB-20 attached to it, a 2A by itself would be a limitation. The MB-20 manual has the diagram and instructions on how to connect with the A-3340 (or 3440, etc)- just need some extra rca-rca cables and spend a little time doing the hookup.
Visually, side by side, a 2A/MB-20 & A-3340 would look great, especially if you like the visual appeal of 8 large illuminated VU meters when doing any musical activities at night (I have a vintage Sansui G-9000 amp, with the same meters, thus I have 12 of them
Anyhow, there are lots of choices, good luck and hopefully you find a good deal on a mixer that accomodates your recording/mixing needs.
(come to think of it, a smaller Tascam M-1508 (vs larger 1516) could be a good choice if you see any around that are well maintained.)