MK, it has been done internally. There are brackets out there, usually for the SE, that permit it. I've seen two types. Some mounted a drive vertically near the expansion slot while others stuck it on top of the upper floppy drive/first internal drive. If you're putting a second drive in the SE, you'll need to adapt the power cable to accommodate two outputs and find a double SCSI cable.
Technically, it would be possible to do this inside other Macs. The Classic I isn't a good choice since it already has a vertical RAM card, but I could see this in a Classic II. Some of the modular Macs could definitely accommodate more than one drive if they were smaller in size (think 90s drives here; many 80s 3.5" hard drives were bulkier).
If you really wanted a bunch of hard drives, you could always take out the floppy drives and build a bracket to replace them. Some Macs wouldn't even need this--an LC would have the room. Just be warned some models, like the LC, don't have external floppy drives, so you'd probably want to plan accordingly (networking, CD-ROM).