plotting – Can this 2D-Venn diagram code–involving Disk–be “upgraded” to a 3D one, involving Sphere?

This is only a start, but is this within your capabilities/understanding?

a={1,0,-1/Sqrt(2)};b={-1,0,-1/Sqrt(2)};c={0,1,1/Sqrt(2)};d={0,-1,1/Sqrt(2)};
Graphics3D({Opacity(1/2),
  Sphere(a,3/2),Sphere(b,3/2),Sphere(c,3/2),Sphere(d,3/2),
  Text("A",a),Text("B",b),Text("C",c),Text("D",d),
  Text("AB",(a+b)/2),Text("AC",(a+c)/2),
  Text("AD",(a+d)/2),Text("BC",(b+c)/2),
  Text("BD",(b+d)/2),Text("CD",(c+d)/2),
  Text("ABC",(a+b+c)/3),Text("ABD",(a+b+d)/3),
  Text("ACD",(a+c+d)/3),Text("BCD",(b+c+d)/3),
  Text("ABCD",(a+b+c+d)/4)
})

Can you see how that was done? Can you see how each part might work?
Can you adjust the Opacity and size and Text size to make that better?
Can anyone else suggest why dragging the box with the mouse doesn’t
seem to correctly show the Text sometimes?

There are a LOT of labels to be able to distinguish in one diagram, but perhaps you can learn a bit from this and make some progress and be better prepared to do other things in the future.