If you want to keep the distances exactly, then no, not really. If you fix 2 points in the plane, and want a third point with prescribed distances from the first two, you only have two options for that third point (symmetric across the line connecting the first two points). This severely constrains even three points; more will almost surely be impossible to graph exactly.
If you want to alter the distances in a way to preserve an order on them (in which I mean: if the distance between a pair of points is greater than that of a second pair of points, this will remain the case after altercation), or see them in more than three dimensions but from various angles or perspectives, then there might be mathematics to help you out there.