My first unicorn would be the hackarific Tandy 1000 SL we had from the early 90's with this awesome sounding Miniscribe 8425F hard drive. I managed to re-acquire a 1000 SL since though, and I came up with my own unique hacks (replacing the SL motherboard with a '286-based 1000 TL board with 80287 FPU, along with the sound op-amp on said board). Currently fitted with an XT-IDE adapter driving a whistling Maxtor 7120AT. Unfortunately I haven't been able to locate a copy of Geoworks Pro to make it like the old one...
Second one, an Everex/AGI 3000G 386SX-16. Owned this waaaay back in about 1994 or 1995. The case was this huge, hulking full-AT desktop, and it had a great super-loud speaker too. The hard drive (a Priam Innerspace ID45H aka. Microscience HH-1050) went out in a blaze of glory and screeching metal, so we elected to have the system more or less totally rebuilt into a 386DX-40 based midtower. The difference in speed between a 386SX-16 and a 386DX-40 was dramatic. That system slowly evolved over time, first upgrade was an Alaris Leopard 486SLC2, next some no-name Socket 3 board that never quite worked right before a cacheless wonder Socket 3 replaced that, running a Trinity Works Powerstacker (Am5x86-133). It sat in my dad's school room doing word processing duty for about a year or two.
Third unicorn, an IBM PS/2 Model 57SLC. Got that from a friend at college, wish I NEVER got rid of it. I remember hacking up a 72-pin SIMM to upgrade the memory! I managed to acquire a 56SLC, which IIRC uses a similar motherboard and is much the same in function, but a fair bit smaller. Unfortunately it didn't come with the really strange 1/2 height 3.5" SCSI drive the 57SLC did. (That drive had a unique seek test racket too, which I have never heard from any other drive, forgot what make/model it was.)
Geez, I'm rambling like that 'Lenny' bot about my old computers. 😜
Life isn't long enough to re-enable every hidden option in every BIOS on every board... 🙁