Based on a result of R. P. Stanley (J. Combin. Theory Ser. B 38, 1985, 132-138) we show that for each s ≥ 4 there exists an integer Ns such that any graph with n > Ns vertices is reconstructible from the multiset of graphs obtained by switching of vertex subsets with s vertices, provided n ≠ 0 (mod 4) if s is odd. We also establish an analog of P. J. Kelly's lemma (Pacific J. Math., 1957, 961-968) for the above s-switching reconstruction problem.