We were still using 5 1/4”, but the school CS teacher had a special press that cut a notch into the 360K (?) ones to trick the Apple II’s into using them in 720K mode.
She also had a utility to copy original software disks onto the “high density” disks, then read back the data.
From what I could tell, it worked like a charm. 10% of the copies failed, but whatever.
(Coursework was stored on unmodified disks, of course.)
The special press was fancy! I used a hole punch (the type intended for punching small round holes in paper), and as long as you lined it up correctly it worked great.
I suspect you're thinking of the Amstrad Spectrum +2 (grey, largely the same as the Sinclair ZX Spectrum 128) vs Amstrad Spectrum +2A (black, contained a +3 motherboard minus the FDD controller, and less compatible with external peripherals).