The lattice-constant of a solid-state material is a key parameter in determining its physical and chemical properties. By varying the lattice constant one can tune the electronic band structure as well as the density of states at the Fermi level, therefore change correspondingly all the physical and chemical properties. In this work, by using the "composition wedge" and "lattice-constant wedge" techniques with molecular beam epitaxy, we show that one can manipulate independently the surface chemistry and lattice constant of a single crystal substrate. Applying them to ultrathin Fe and Ni on Cu(001), two of the most important yet still controversial nanomagnetic systems, we show how to manipulate their magnetic properties including magnetic ordering and anisotropy in a well controlled way which is helpful to clarify some longstanding critical issues of the systems.