That Korg looks does a simplified version of what you want. No individual track preservation, so not really "4 track Portastudio style", only additive sound-on-sound stereo layering.
I'd did this for grins using two Tascam DR2d recorders and a stereo-mini patch cable a few years ago. That works since the DR2d can be set to record two stereo inputs (or internal mics + external stereo input) and mix the two to a single recorded file. By patching the output of the recorder doing the playback into the line-input of the one used for recording the bounce + the new material, I could bounce back and forth between the two machines adding an additional part each time. That means a D>A>D conversion each bounce, so besides each addition being non-reversible, there is some degredation each generation. Not dissimilar in that way to additive tape generation degradation each bounce, but not nearly as severe or noisy.
That's basically the functionality the Korg provides, except the Korg would be a far better choice for doing that kind of thing regularly. I did it partly because I tried doing the same thing way back in the 80's using two cassette Walkman recorders, which worked but got so horribly hissy after just a couple bounces it was unpractical.
You're probably best off buying a dedicated stereo recorder for field recordings and looking for a separate memory card based mulitchannel recorder intended for song composition. Not sure what's available in that department these days, but there were numerous versions of that available just a few years ago. Basically just smaller memory card versions of the old cassette Portastudios. Most of those that I saw typically didn't record at as high a rate as dedicated 2-channel stereo recorders though, typically maxing out at 44.1kHz/16bit.