You can install a high density floppy drive in an A600. The specific capacity isn't 1.44(MB) though, that's for PCs. (Or to be precise it's 1440KB, or 1.41MB.) But Amiga high density floppys are 1760KB, or 1.72MB. I have a Sony model MPF920-E high density drive in my A1200. It doesn't require any special board or driver, it's just plugged in at the usual floppy bay where the original 880KB one would be. I'd be surprised if this is any different for an A600.
Hi Mizar, you can't use your Sony MPF920-E at 1.72MB though ?