non-reduced configurations of lines in general position in projective space

A well-known theorem by hartshorne and hirschowitz states that a generic configuration of lines in $pp^n$, $ngeq 3$, has good postulation. so a natural question in studying the postulation of non-reduced linear configurations is: can adding a non-reduced component to the configuration still preserve it's good postulation? this is what we investigate here.we study the postulation of a generic configuration of lines and one multiple line. we solve the case of lines and one double line, and give a conjecture to the general case.