I haven’t found a way yet. Trick could be to interpolate with a distance less than your points are apart, then you get a series of regularly spaced handles that do not do anything for the edges you are not interested in, but gives you new handles to move about.
Via macro it would be possible to add one point between each point pair you have on the polygon, then ignore the ones you are not interested in.
I’ve made a macro in the past that after activation follows the cursor along the nearest point of the ROI and does something (add a point in your case) when you click the mouse. Briefly, you add the ROI to the ROI manager in order to keep it in its original state, interpolate the ROI with a step of 1 in the image, get the coordinates of (then) all points on the ROI, do some math to deduce the point nearest the cursor but on the ROI and wait for a click. Then take the currently active point on the roi and insert its coordinates in between the pair of the original polygon. Involved? Yes. Impossible? No.
Probably there is an easier method, but I stick to ImageJ1 macro language.