"Extending our previous work (Rosu, Mancas, Chen, Ann.Phys. 343 (2014) 87-102), we define supersymmetric partner potentials through a particular Riccati solution of the form F(x) = (x − c)2 − 1, where c is a real shift parameter, and work out the quartic double-well family of oneparameter isospectral potentials obtained by using the corresponding general Riccati solution. For these parametric double well potentials, we study how the localization properties of the two wells depend on the parameter of the potentials for various values of the shifting parameter. We also consider the supersymmetric parametric family of the first double-well potential in the Razavy chain of double well potentials corresponding to F(x) = 1/2 sinh 2x−2 (1+p2) sinh 2x/(1+p2) cosh 2x+1 , both unshifted and shifted, to test and compare the localization properties."