The aim of this paper is to derive stable generalized sampling in a shift-invariant space with ℓ stable generators. This is done in the light of the theory of frames in the product Hilbert space Lℓ2(0,1):=L2(0,1)×⋯×L2(0,1) (ℓ times). The generalized samples are expressed as the frame coefficients of an appropriate function in Lℓ2(0,1) with respect to some particular frame in Lℓ2(0,1). Since any multiply stable generated shift-invariant space is the image of Lℓ2(0,1) by means of a bounded invertible operator, the generalized sampling is obtained from some dual frame expansions in Lℓ2(0,1). An example in the setting of the Hermite cubic splines is exhibited.