How to rotate an object in more than one direction?

I have successfully managed to rotate an object along one axis (pitch, yaw and roll), but when I try to combine multiple rotations, it isn’t performing the way I want, or think it should.

Basically if I were to rotate the object let’s say along Axis one, it would take on values:
(1,0,0) to (0,1,0) to (-1,0,0) to (0,-1,0) and all the points in-between relative to the X and Y values.

And for another axis, it would be for example:
(1,0,0) to (0,0,1) to (-1,0,0) to (0,0,-1)

Now when combining these two rotations, I want there to be at some point in the rotation (this could be seconds or hours in) where all 8 points above are obtained. That is, at some point of the two rotations, the object would have rotated to (-1,0,0).

Now, I can’t see to get this working. The rotations seem to be combined that the object doesn’t rotate along each axes separately (together), but a rotation is occurring along some new axis created via these rotation angles. So all 8 points mentioned earlier will never be achieved.