Split a single drawing into multiple bodies

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I have a file which has a single body part that I now want to split.
I created a file which I used to test splitting. It is attached.
In this example, I
(a) created a sketch
(b) placed a circle on it
(c) closed the sketch
(d) extruded the circle into a 30mm rod
(e) placed a work plane relative to the end of the rod, 15mm
(f) Selected the split command
(g) selected split solid body
(h) selected the split tool to be the work plane
(i) clicked OK
(j) selected move bodies
(k) moved the selected body 10mm from the other part
The result is that I now have a single rod which has been split into two bodies. OK, I understand that.
I then
(a) edited the sketch
(b) placed the square
(c) closed the sketch
(d) extruded the square profile into a 30mm rod; to make this work, I had to indicate which body it was going to be part of. I selected the (as shown in this screen snapshot) the "left" body I created in the first phase.
I now have a drawing that has two bodies: half the circular rod; the other half of the circular rod combined with the square rod
Now, assume I realize I have made a mistake. I want to have three bodies. So I
(a) create a work plane based on one side of the square rod, positioned about 5mm away.
(b) select the Split command
(c) select solid bodies
(d) select the body by clicking on the round rod that has the square rod as part of the body
(e) select the split tool to be the work plane
(f) click OK
I get the error message shown on the screen shot.
The real problem is that the two parts are not round rod and square rod, but complex drawing 1 and complex drawing 2. I want to split these two disjoint drawings into two bodies. So I created the simplest case that reproduced the problem I have.