In this work we consider the class of partially integrable 3-dimensional piecewise smooth vector fields \(Y=(X^+,X^-)\) with separation set \(\Sigma =\{(x,y,z)\in {\mathbb {R}}^3: z=0\}\) and first integral \(H(x,y,z)=x^2+y^2+z^2\) that leaves invariant any sphere centered at the origin, \({\mathbb {S}}_\rho ^2=\{(x,y,z)\in {\mathbb {R}}^3: x^2+y^2+z^2=\rho ^2\}\) . We denote this class by \(\mathcal {X}\) and by \(\mathcal {X}_n\) when \(X^\pm \) are polynomial vector fields of degree n. Our main goal is to study piecewise smooth vector fields in the class \(\mathcal {X}_1\) presenting three periodic annuli on the invariant sphere \({\mathbb {S}}_1^2\) proving that there exists a mixed simultaneous configuration with at least five limit cycles bifurcating simultaneously of them, considering polynomial perturbations inside the class \(\mathcal {X}_2\) .
