Keep in mind a circle is simply an ellipse. So you can still do this as an ellipse where the circular profile happens to have the same dimensions in X and Y axes, and the X and Y axes are controlled by one guide curve each. Similarly, you can sweep with two half-ellipses to have a final shape that differs from front to back--or in quarter-ellipses, etc.
(I used to have to do this sort of thing frequently to make good handles/hand-grips for products over ten years ago before surfacing tools became more robust.)