Answers,...
You may often find good used 246's in like-new condition and 100% functional, if you watch Ebay/Tascam often enough. The 246 is one of the most feature-rich and capable 4-track Portastudio, ever, recording 6-channels to 4-tracks in "Buss" mode. Average price on the Tascam 246 would be appx. $125/used.
There's the Tascm 644, which also records 4-tracks/simul from a 16 input mixer, with tape-sync and midi functions built in,... but you'll need the manual to learn to operate it. Average cost on the 644 is appx. $150~$200/used.
The brand new 4-track cassette recorders are becoming a dying breed, with the 424mkIII already having gone out of production and off retailers shelves.
The "best" brand new 4-track cassette that's now avialable is the 414mkII, which records up to 4-tracks simultaneously in Direct mode, (2-tracks/simul in Buss-mode). Brand new price on the 414mkII is $249, but average Ebay price is more like $80, (your choice).
However, the 424mkIII is trading briskly on Ebay,... most in like-new condition,... for about $150/used, average, which is a great deal. The 424mkIII is a significantly upgrade over the 414mkII. The 424mkIII records up to 4-tracks/simul in Direct-mode, and 2-tracks/simul in Buss-mode.
Then, there's the 424mkII, which is a slightly older version than the 424mkIII, but is a relative steal at appx. $100/used. It has virtually e'thing the 424mkIII has,... less the 2 extra "full" channel strips.
Vestax and Sansui both made a 6-track cassette format multitracker, but they're rare and hard to find.
If u r a bit more adventurous, or crave more hifi than a 2X speed cassette can offer, then maybe you should consider the 1/4"-reel Tascam 388 or perhaps the 34B.
The 388 is a true "Portastudio" format unit, that records up to 8-tracks simultaneously onto 7" reels of 1/4" tape.
The 34B is a larger reel/reel recorder that records either from a mixer's outputs on RCA jacks, or from it's own built-in mic preamps on 1/4" phone jacks, at either 7.5 or 15 ips and uses either 7" or 10.5" reels of 1/4" tape.
...
PS: Cannot forget to mention the Tascam 488mkII & the 688. The 688 is the high techiest Portastudio ever, which has a 20 input mixer and records 8-tracks simultaneously. The 688 has about a hundred buttons, tape-sync and midi functions, and the manual's a must!!!
The 488mkII is slightly less intense than the 688, but is still a good unit which records up to 4-tracks/simul in Buss mode.
For cassette 8-tracks (8-in/8-out/8-simul) that's rack mountable and requires an external mixer, check the Tascam 238.
...
So check'em out, eh?
/DA