adjust freeform gradient to have a specific color at every point along edge of object

I'm trying to construct an illstrator object that uses freeform gradients but where at every possible edge point of the object, the object has a specific color so that it seemlessly and smoothly transitions from the object edge to the background color.

To make it particularly simple, lets say that I have a rectangle with some freeform gradient points or lines where the colors of the points are reds, blues, greens, etc. But I want every point at the edge of the rectangle to be white so that the gradient smoothly transitions to a white background, and when the object say is rendered on a web page, one can't tell the point that the object ends and background begins (i.e., no edge artifacts or evidence of edge points at all). 

Is this something that is possible as I've searched around and have not been able to find a solution to this problem. Thanks very much.