In the article, we consider a point controllability over all (infinite many) passes for linear differential repetitive processes. We prove the following approximative piecewise constant bang-bang principle: the set of points that can be reached with the aid of measurable controls on passes, taking the values in a convex compact set M r coincides with the closure of the set of points that can be reached with the aid of piecewise constant controls on passes, taking the values in the set of extreme points of M.