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A (2+1)-dimensional
N
-coupled nonlinear Schrödinger equation with spatially modulated cubic–quintic nonlinearity and transverse modulation is studied, and vector multipole and vortex soliton solutions are analytically obtained. When the modulation depth
q
is chosen as 0 and 1, vector multipole and vortex solitons are constructed, respectively. The number of “petals” for the multipole solitons and vortex solitons is related to the value of the topological charge
m
, and the number of layers in the multipole solitons and vortex solitons is determined by the value of the soliton order number
n
.