In a previous paper, it was demonstrated that any linear system could
be made to respond to harmonic excitation as if a static nonlinearity
of specified type and position were present, this response being obtai
ned at a single predetermined point on the structure. The method requi
res the excitation of the linear structure by an additional or auxilia
ry input. In the present paper, the theory is extended to allow the po
ssibility of producing a specified nonlinear response at more than one
point on a linear structure. It is shown that N responses can be obta
ined by specifying N or less auxiliary inputs. The theory is also exte
nded to provide for polynomial damping in addition to stiffness nonlin
earity. The theory is validated using numerical simulation of MDOF lum
ped-parameter systems.