Are the mouthpieces from other instruments interchangeable with the clarinet? For example can I use an Allto sax mouthpiece or ligature or cap on an alto clarinet, or a soprano sax mouthpiece or ligature or cap on a soprano clarinet? Will it fit on and will it sound right?
Interchangeable is a bit strong. Some equipment will fit instruments other than the instrument it was designed for. Bb clarinet ligatures will work on many HR alto sax mouthpieces. Some soprano sax ligatures will work on metal tenor sax mouthpieces.
There is no rule saying you cannot try something on anything, but don't force anything into or over anything it wasn't designed to be used with.
Mouthpieces themselves seldom work on other instruments, with the exception of C saxophones and alto/tenor mouthpieces, most don't work well on other instruments.