Recently, several remarkable works [1]-[5] constructed regenerating codes to offer intermediate tradeoffs between storage and bandwidth. Unlike regenerating codes, this paper proposes to graft codes together to provide various such intermediate tradeoffs. It shows that the linear relations in the generator matrices of grafting codes can be transferred to those of grafted codes without any loss of reconstruction capability. A construction based on minimum storage regenerating codes shows that the resulted graftage codes may provide better tradeoffs than space-sharing and approach cut-set bounds, with the cost of fixed access of helper nodes.