In Simplex Method, can I move from a basic solution $x^{*}$ to the other $y^{*}$ by pivoting zero cost in Tableau?

Suppose that $$B_1$$ is the bases for $$x^{*}$$ and I want to go to the second solution $$y^{*}$$ with bases $$B_2$$, how to go to the second optimal solution through pivoting? My attempt was trying to prove that the reduced costs of the variables in bases $$B_2$$ is zero, but it was unsuccessful.