Sure you can.

What make and type is your 4-track deck? Does it have an onboard mixer like the Fostex 260. If not than you'll need a little mixer, of at least 4 channels and possibly a couple of auxes if you want to ad FX.

I had a Fostex 260 back in 86 and did that very thing. I used a Technics BS655 or so stereo cassettedeck to mix down on, with DBX noise suppression on and a metal type tape inside. That was until we had a DAT-recorder.

I even used that as an in between stage to be able to add another two tracks and still keep it stereo. You can even add an acoustic guitar, handclaps or percussion in the process if you can play the whole part in one go.

I still have an old Tascam Porta One by my couch that I punch record on when I find a new lick.
I started out with it, and learned some guerilla recording tactics.
I used to mix down to a Hi-Fi VCR, (through a small mixer, adding another track as I went). It's a bit cumbersome, but just record a count-in before the tune so you know when to start. It actually didn't sound all that bad. Probably better than cassette to cassette.
Once the four tracks, plus the added track, was on the VCR tape, in stereo, I ran that back through the mixer while adding another track, to record to two tracks of the Tascam...on the next part of the tape.

Depending on how many times I thought I would need to bounce, I tried something I read once. I think it was a George Martin trick, or something.
Knowing it was going to lose a bit of high-end on each bounce back to the cassette, I bounced it to the VCR a teeny bit bright. Not enough to produce sibilance and other nasty stuff, just a teeny bit. That seemed to work fairly well, and the earlier tracks kept a lot of their range. I think I only ever bounced twice, so I didn't need too much.

The Tascam Porta One has four individual direct track outs, and also a stereo mix out. I usually used the mix out, because it was post-fader, post-EQ, it used only two tracks of the small mixer, and I could use the tone controls. Ahh, the good ol' days.

Just something to think about.

Kapt.Krunch

P.S. Forgot to add that this was all B.C. (before computer). Why not just dump it into a computer, and play it back. Even a Soundblaster would be easier and probably sound at least as good as a cassette or VCR.