We consider a class of (2+1)-dimensional baby Skyrme models with potentials that have more than one vacuum. These potentials are generalizations of the old and new baby Skyrme models in that they involve a more complicated dependence on φ₃ (V(φ₃)≥0). The boundary conditions are such that φ₃ = 1 corresponds to the vacuum and φ₃ = -1 at the position of each skyrmion. We find that when the potential vanishes at φ₃ = -1 the configurations corresponding to the baby skyrmions lying `on top of each other' are the minima of the energy. However, when V(φ₃ = -1)0 the lowest field configurations correspond to separated baby skyrmions. We determine the energy distributions for skyrmions of degrees between one and eight and discuss their geometrical shapes and binding energies. We also compare the two-skyrmion states for these potentials. Most of our work has been performed numerically with the model being formulated in terms of three real scalar fields (satisfying one constraint).