The 386 portable has no internal slots. I *do* have the expansion chassis (a large "bag" that bolts on the back) -- but it only supports two slots and I have a double-wide card that usually sits in there.
A better move is a PATA-SATA adapter (I think I have some of those... or, maybe they are SCA-SCSI or FW or... <shrug>)
But, you're still stuck with the limitations of the old BIOS -- which had no "user defined" disk geometry (and dates from the days when the PC told the drive what it's geometry would be). To support the
600M drive, I had to edit the BIOS EPROMs (yes, that's how old it is!) and fix the checksum so my changes didn't signal a POST fault. [Or, maybe it was 340M like the "spare" I have? I can't recall. Booting it to check would be tedious as the BBRAM is failed (used a large battery for that, back then, made in Israel, IIRC). And, "setup" resides on a 5" floppy just to get in and set the parameters... Yes, only of value to collectors! But, a small footprint way for me to support a pair of ISA slots!]