Kind of a similar story to the Commodore PCs, which could be less incompatible with their other lines (ST and Amiga), and have some part commonality to save costs (same keyboards, same monitors), maybe better graphics, and, eventually, serve as a bridge out of their proprietary sinking ships.
I can't imagine why an Amiga 2000 case couldn't hold a PC motherboard or why a Mega ST keyboard couldn't be a PS/2 keyboard (and an Atari mouse be a PS/2 mouse). It wouldn't be that easy for an Amiga to read/write PC disks, but it'd be worth the effort.
There are DOS drivers for AmigaOS, IIRC they were even bundled from 2.x on.
There are some mashups between the architectures (Vortex cards for Mega STe, Amiga Sidecars...) but they were either expensive or unsuccessful.
I can't imagine why an Amiga 2000 case couldn't hold a PC motherboard or why a Mega ST keyboard couldn't be a PS/2 keyboard (and an Atari mouse be a PS/2 mouse). It wouldn't be that easy for an Amiga to read/write PC disks, but it'd be worth the effort.